Find $lim_n to inftyleft(frac(3n)!(2n)!n^nright)^1/n$ [closed]

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
-1
down vote

favorite












Find $$lim_n to inftyleft(frac(3n)!(2n)!n^nright)^1/n$$




sequences-and-series




share|cite|improve this question













closed as off-topic by user223391, Batominovski, Siong Thye Goh, José Carlos Santos, heropup Jul 30 at 7:54


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Batominovski, Siong Thye Goh, José Carlos Santos, heropup
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 1




    Please see math.meta.stackexchange.com/questions/5020
    – Lord Shark the Unknown
    Jul 30 at 6:44














up vote
-1
down vote

favorite












Find $$lim_n to inftyleft(frac(3n)!(2n)!n^nright)^1/n$$




sequences-and-series




share|cite|improve this question













closed as off-topic by user223391, Batominovski, Siong Thye Goh, José Carlos Santos, heropup Jul 30 at 7:54


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Batominovski, Siong Thye Goh, José Carlos Santos, heropup
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 1




    Please see math.meta.stackexchange.com/questions/5020
    – Lord Shark the Unknown
    Jul 30 at 6:44












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











Find $$lim_n to inftyleft(frac(3n)!(2n)!n^nright)^1/n$$




sequences-and-series




share|cite|improve this question













Find $$lim_n to inftyleft(frac(3n)!(2n)!n^nright)^1/n$$





sequences-and-series





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 30 at 6:54









Bill O'Haran

2,4411418




2,4411418









asked Jul 30 at 6:38









Afif bakr

11




11




closed as off-topic by user223391, Batominovski, Siong Thye Goh, José Carlos Santos, heropup Jul 30 at 7:54


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Batominovski, Siong Thye Goh, José Carlos Santos, heropup
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by user223391, Batominovski, Siong Thye Goh, José Carlos Santos, heropup Jul 30 at 7:54


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Batominovski, Siong Thye Goh, José Carlos Santos, heropup
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 1




    Please see math.meta.stackexchange.com/questions/5020
    – Lord Shark the Unknown
    Jul 30 at 6:44












  • 1




    Please see math.meta.stackexchange.com/questions/5020
    – Lord Shark the Unknown
    Jul 30 at 6:44







1




1




Please see math.meta.stackexchange.com/questions/5020
– Lord Shark the Unknown
Jul 30 at 6:44




Please see math.meta.stackexchange.com/questions/5020
– Lord Shark the Unknown
Jul 30 at 6:44










1 Answer
1






active

oldest

votes

















up vote
2
down vote













Given $$lim_nrightarrow inftybigg[frac(3n)!(2n)!cdot n^nbigg]^frac1n$$



Using stirling approximation $$n!=bigg(fracnebigg)^frac1nsqrt2pi n$$



So $$lim_nrightarrow inftyBigg[fracbigg(frac3nebigg)^3nsqrt6pi nbigg(frac2nebigg)^2nsqrt4pi ncdot n^nBigg]^frac1n.$$



So $$lim_nrightarrow inftyfrac274ebigg(fracsqrt6pi nsqrt2pi nbigg)^frac1n=frac274e.$$






share|cite|improve this answer



















  • 1




    You mean: $enspacedisplaystyle n!approxleft(fracneright)^nsqrt2pi nenspace$
    – user90369
    Jul 30 at 7:29











  • Some $e$ got lost in the last passage.
    – Saucy O'Path
    Jul 30 at 7:53


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
2
down vote













Given $$lim_nrightarrow inftybigg[frac(3n)!(2n)!cdot n^nbigg]^frac1n$$



Using stirling approximation $$n!=bigg(fracnebigg)^frac1nsqrt2pi n$$



So $$lim_nrightarrow inftyBigg[fracbigg(frac3nebigg)^3nsqrt6pi nbigg(frac2nebigg)^2nsqrt4pi ncdot n^nBigg]^frac1n.$$



So $$lim_nrightarrow inftyfrac274ebigg(fracsqrt6pi nsqrt2pi nbigg)^frac1n=frac274e.$$






share|cite|improve this answer



















  • 1




    You mean: $enspacedisplaystyle n!approxleft(fracneright)^nsqrt2pi nenspace$
    – user90369
    Jul 30 at 7:29











  • Some $e$ got lost in the last passage.
    – Saucy O'Path
    Jul 30 at 7:53















up vote
2
down vote













Given $$lim_nrightarrow inftybigg[frac(3n)!(2n)!cdot n^nbigg]^frac1n$$



Using stirling approximation $$n!=bigg(fracnebigg)^frac1nsqrt2pi n$$



So $$lim_nrightarrow inftyBigg[fracbigg(frac3nebigg)^3nsqrt6pi nbigg(frac2nebigg)^2nsqrt4pi ncdot n^nBigg]^frac1n.$$



So $$lim_nrightarrow inftyfrac274ebigg(fracsqrt6pi nsqrt2pi nbigg)^frac1n=frac274e.$$






share|cite|improve this answer



















  • 1




    You mean: $enspacedisplaystyle n!approxleft(fracneright)^nsqrt2pi nenspace$
    – user90369
    Jul 30 at 7:29











  • Some $e$ got lost in the last passage.
    – Saucy O'Path
    Jul 30 at 7:53













up vote
2
down vote










up vote
2
down vote









Given $$lim_nrightarrow inftybigg[frac(3n)!(2n)!cdot n^nbigg]^frac1n$$



Using stirling approximation $$n!=bigg(fracnebigg)^frac1nsqrt2pi n$$



So $$lim_nrightarrow inftyBigg[fracbigg(frac3nebigg)^3nsqrt6pi nbigg(frac2nebigg)^2nsqrt4pi ncdot n^nBigg]^frac1n.$$



So $$lim_nrightarrow inftyfrac274ebigg(fracsqrt6pi nsqrt2pi nbigg)^frac1n=frac274e.$$






share|cite|improve this answer















Given $$lim_nrightarrow inftybigg[frac(3n)!(2n)!cdot n^nbigg]^frac1n$$



Using stirling approximation $$n!=bigg(fracnebigg)^frac1nsqrt2pi n$$



So $$lim_nrightarrow inftyBigg[fracbigg(frac3nebigg)^3nsqrt6pi nbigg(frac2nebigg)^2nsqrt4pi ncdot n^nBigg]^frac1n.$$



So $$lim_nrightarrow inftyfrac274ebigg(fracsqrt6pi nsqrt2pi nbigg)^frac1n=frac274e.$$







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited Jul 30 at 9:29


























answered Jul 30 at 6:52









Durgesh Tiwari

4,7782426




4,7782426







  • 1




    You mean: $enspacedisplaystyle n!approxleft(fracneright)^nsqrt2pi nenspace$
    – user90369
    Jul 30 at 7:29











  • Some $e$ got lost in the last passage.
    – Saucy O'Path
    Jul 30 at 7:53













  • 1




    You mean: $enspacedisplaystyle n!approxleft(fracneright)^nsqrt2pi nenspace$
    – user90369
    Jul 30 at 7:29











  • Some $e$ got lost in the last passage.
    – Saucy O'Path
    Jul 30 at 7:53








1




1




You mean: $enspacedisplaystyle n!approxleft(fracneright)^nsqrt2pi nenspace$
– user90369
Jul 30 at 7:29





You mean: $enspacedisplaystyle n!approxleft(fracneright)^nsqrt2pi nenspace$
– user90369
Jul 30 at 7:29













Some $e$ got lost in the last passage.
– Saucy O'Path
Jul 30 at 7:53





Some $e$ got lost in the last passage.
– Saucy O'Path
Jul 30 at 7:53



Comments

Post a Comment

Popular posts from this blog

What is the equation of a 3D cone with generalised tilt?

Image
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin $(0,0,0)$ - I was wondering if anyone could give me a more generalized cone equation for a cone in any position in 3D space 3d share | cite | improve this question edited Jul 25 '16 at 0:05 ervx 9,425 3 13 36 asked Jul 24 '16 at 15:38 Charlene 11 2 2 Welcome to Math.SE! Could you please explain a few things to help people give an answer useful to you: 1. What do you mean by "generalized tilt"? 2. Are you asking about a right circular cone? Does the angle at the vertex matter? 3. What form of answer (implicit, parametric...?) are you looking for? 4. If this is homework, what tools do you have available, an...
Read more

Relationship between determinant of matrix and determinant of adjoint?

Image
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite We are studying adjoints in class, and I was curious if there is a relationship between the determinant of matrix A, and the determinant of the adjoint of matrix A? I assume there would be a relationship because finding the adjoint requires creating a cofactor matrix and then transposing it. linear-algebra determinant adjoint-operators share | cite | improve this question asked Nov 17 '17 at 17:32 CluelessCoder 32 5 For a square matrix $A$ of order $n$, we have $A(operatornameadj A)=(operatornameadj A)A=|A|I_n$ where $I_n$ is the identity matrix of order $n$. This should tell you about the determinant of the adjoint in terms of that of $A$ (use multiplicative property and other elementary properties of determinants). – Prasun Biswas Nov 17 '17 at 17:35 1 @CluelessCoder: see here: math.stackexchange.com/questions/516127/…...
Read more

Color the edges and diagonals of a regular polygon

Image
Clash Royale CLAN TAG #URR8PPP up vote 5 down vote favorite 1 Here is the problem: For what $n$ is it possible to color the edges and diagonals of an $n$-side regular polygon with $dfracbinomn23$ colors, such that you use every color exactly three times and for every color the three segments (edges or diagonals) with that color form a triangle? Trivially $nequiv 0 text or 1 pmod3$. I can also prove that if the statement is true for $k$ than it is true for $3k$ as well. How to finish? Please help! Thanks combinatorial-geometry share | cite | improve this question edited Aug 6 at 21:57 alcana 118 4 asked Aug 6 at 21:15 Leo Gardner 356 11 Even assuming "polyhpn" in the title is a typo for polygon , it is unclear what you mean by "the edges and sides". Aren't the side of a regular polygon the same as the edges? A regular $n$-sided polygon has $n$ edges. – hardmath Aug 6 at 21:20 3 $n$ ne...
Read more