Calculate $lim_n rightarrow infty sum_n=0^infty(-1)^n frac12^n$

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Calculate



$lim_n rightarrow infty$ $sum_n=0^infty$$(-1)^n$$ frac 12^n$



my attempt :
beginalignlim_n rightarrow inftysum_n=0^infty(-1)^n frac 12^n&=lim_n rightarrow infty(-1)^n( 1+ 1/2 + 1/2^2 +dots+ 1/2^n)\
&=lim_n rightarrow infty(-1)^nfrac ( 1-(1/2)^n) 1-1/2\
&=lim_n rightarrow infty(-1)^n2
endalign



Is it correct ??? as Im not able to proceed Further Pliz help me....




real-analysis




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  • 1




    Your first equality is wrong.
    – José Carlos Santos
    Jul 19 at 9:11














up vote
0
down vote

favorite












Calculate



$lim_n rightarrow infty$ $sum_n=0^infty$$(-1)^n$$ frac 12^n$



my attempt :
beginalignlim_n rightarrow inftysum_n=0^infty(-1)^n frac 12^n&=lim_n rightarrow infty(-1)^n( 1+ 1/2 + 1/2^2 +dots+ 1/2^n)\
&=lim_n rightarrow infty(-1)^nfrac ( 1-(1/2)^n) 1-1/2\
&=lim_n rightarrow infty(-1)^n2
endalign



Is it correct ??? as Im not able to proceed Further Pliz help me....




real-analysis




share|cite|improve this question

















  • 1




    Your first equality is wrong.
    – José Carlos Santos
    Jul 19 at 9:11












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Calculate



$lim_n rightarrow infty$ $sum_n=0^infty$$(-1)^n$$ frac 12^n$



my attempt :
beginalignlim_n rightarrow inftysum_n=0^infty(-1)^n frac 12^n&=lim_n rightarrow infty(-1)^n( 1+ 1/2 + 1/2^2 +dots+ 1/2^n)\
&=lim_n rightarrow infty(-1)^nfrac ( 1-(1/2)^n) 1-1/2\
&=lim_n rightarrow infty(-1)^n2
endalign



Is it correct ??? as Im not able to proceed Further Pliz help me....




real-analysis




share|cite|improve this question













Calculate



$lim_n rightarrow infty$ $sum_n=0^infty$$(-1)^n$$ frac 12^n$



my attempt :
beginalignlim_n rightarrow inftysum_n=0^infty(-1)^n frac 12^n&=lim_n rightarrow infty(-1)^n( 1+ 1/2 + 1/2^2 +dots+ 1/2^n)\
&=lim_n rightarrow infty(-1)^nfrac ( 1-(1/2)^n) 1-1/2\
&=lim_n rightarrow infty(-1)^n2
endalign



Is it correct ??? as Im not able to proceed Further Pliz help me....





real-analysis





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edited Jul 19 at 9:58









Bernard

110k635103




110k635103









asked Jul 19 at 9:00









stupid

55819




55819







  • 1




    Your first equality is wrong.
    – José Carlos Santos
    Jul 19 at 9:11












  • 1




    Your first equality is wrong.
    – José Carlos Santos
    Jul 19 at 9:11







1




1




Your first equality is wrong.
– José Carlos Santos
Jul 19 at 9:11




Your first equality is wrong.
– José Carlos Santos
Jul 19 at 9:11










1 Answer
1






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up vote
6
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$sum_n=0^infty(-1)^n frac12^n=sum_n=0^infty(- frac12)^n$.



Geometric series !






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  • can u elaborate the answer more ,,,@Fred
    – stupid
    Jul 19 at 9:21











  • $sum_n=0^inftyq^n=(1-q)^-1$ for $|q|<1$.
    – Fred
    Jul 19 at 9:26











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1 Answer
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up vote
6
down vote













$sum_n=0^infty(-1)^n frac12^n=sum_n=0^infty(- frac12)^n$.



Geometric series !






share|cite|improve this answer





















  • can u elaborate the answer more ,,,@Fred
    – stupid
    Jul 19 at 9:21











  • $sum_n=0^inftyq^n=(1-q)^-1$ for $|q|<1$.
    – Fred
    Jul 19 at 9:26















up vote
6
down vote













$sum_n=0^infty(-1)^n frac12^n=sum_n=0^infty(- frac12)^n$.



Geometric series !






share|cite|improve this answer





















  • can u elaborate the answer more ,,,@Fred
    – stupid
    Jul 19 at 9:21











  • $sum_n=0^inftyq^n=(1-q)^-1$ for $|q|<1$.
    – Fred
    Jul 19 at 9:26













up vote
6
down vote










up vote
6
down vote









$sum_n=0^infty(-1)^n frac12^n=sum_n=0^infty(- frac12)^n$.



Geometric series !






share|cite|improve this answer













$sum_n=0^infty(-1)^n frac12^n=sum_n=0^infty(- frac12)^n$.



Geometric series !







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Jul 19 at 9:04









Fred

37.4k1237




37.4k1237











  • can u elaborate the answer more ,,,@Fred
    – stupid
    Jul 19 at 9:21











  • $sum_n=0^inftyq^n=(1-q)^-1$ for $|q|<1$.
    – Fred
    Jul 19 at 9:26

















  • can u elaborate the answer more ,,,@Fred
    – stupid
    Jul 19 at 9:21











  • $sum_n=0^inftyq^n=(1-q)^-1$ for $|q|<1$.
    – Fred
    Jul 19 at 9:26
















can u elaborate the answer more ,,,@Fred
– stupid
Jul 19 at 9:21





can u elaborate the answer more ,,,@Fred
– stupid
Jul 19 at 9:21













$sum_n=0^inftyq^n=(1-q)^-1$ for $|q|<1$.
– Fred
Jul 19 at 9:26





$sum_n=0^inftyq^n=(1-q)^-1$ for $|q|<1$.
– Fred
Jul 19 at 9:26













 

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