Mixing
finite sequences
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If $ x_1,x_2,cdots x_n $ are $n$ non-zero real numbers such that $(x_1^2+x_2^2+cdots+x_n-1^2)(x_2^2+x_3^2+cdots+x_n^2)le(x_1x_2+x_2x_3+cdots+x_n-1x_n)^2$ then show that $ x_1,x_2,cdots,x_n$ are in G.P
Please give some hints so,that I can solve it
sequences-and-series
asked Jul 18 at 15:39
Apurv
324
add a comment |Â
up vote
-2
down vote
favorite
If $ x_1,x_2,cdots x_n $ are $n$ non-zero real numbers such that $(x_1^2+x_2^2+cdots+x_n-1^2)(x_2^2+x_3^2+cdots+x_n^2)le(x_1x_2+x_2x_3+cdots+x_n-1x_n)^2$ then show that $ x_1,x_2,cdots,x_n$ are in G.P
Please give some hints so,that I can solve it
sequences-and-series
asked Jul 18 at 15:39
Apurv
324
What is G.P?...
– Mostafa Ayaz
Jul 18 at 15:42
en.m.wikipedia.org/wiki/Geometric_progression
– Apurv
Jul 18 at 15:43
Use the Cauchy-Schwarz inequality.
– Somos
Jul 18 at 17:03
add a comment |Â
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
If $ x_1,x_2,cdots x_n $ are $n$ non-zero real numbers such that $(x_1^2+x_2^2+cdots+x_n-1^2)(x_2^2+x_3^2+cdots+x_n^2)le(x_1x_2+x_2x_3+cdots+x_n-1x_n)^2$ then show that $ x_1,x_2,cdots,x_n$ are in G.P
Please give some hints so,that I can solve it
sequences-and-series
asked Jul 18 at 15:39
Apurv
324
If $ x_1,x_2,cdots x_n $ are $n$ non-zero real numbers such that $(x_1^2+x_2^2+cdots+x_n-1^2)(x_2^2+x_3^2+cdots+x_n^2)le(x_1x_2+x_2x_3+cdots+x_n-1x_n)^2$ then show that $ x_1,x_2,cdots,x_n$ are in G.P
Please give some hints so,that I can solve it
sequences-and-series
asked Jul 18 at 15:39
Apurv
324
asked Jul 18 at 15:39
Apurv
324
asked Jul 18 at 15:39
Apurv
324
asked Jul 18 at 15:39
Apurv
324
324
What is G.P?...
– Mostafa Ayaz
Jul 18 at 15:42
en.m.wikipedia.org/wiki/Geometric_progression
– Apurv
Jul 18 at 15:43
Use the Cauchy-Schwarz inequality.
– Somos
Jul 18 at 17:03
add a comment |Â
What is G.P?...
– Mostafa Ayaz
Jul 18 at 15:42
en.m.wikipedia.org/wiki/Geometric_progression
– Apurv
Jul 18 at 15:43
Use the Cauchy-Schwarz inequality.
– Somos
Jul 18 at 17:03
What is G.P?...
– Mostafa Ayaz
Jul 18 at 15:42
What is G.P?...
– Mostafa Ayaz
Jul 18 at 15:42
en.m.wikipedia.org/wiki/Geometric_progression
– Apurv
Jul 18 at 15:43
en.m.wikipedia.org/wiki/Geometric_progression
– Apurv
Jul 18 at 15:43
Use the Cauchy-Schwarz inequality.
– Somos
Jul 18 at 17:03
Use the Cauchy-Schwarz inequality.
– Somos
Jul 18 at 17:03
add a comment |Â
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What is G.P?...
– Mostafa Ayaz
Jul 18 at 15:42
en.m.wikipedia.org/wiki/Geometric_progression
– Apurv
Jul 18 at 15:43
Use the Cauchy-Schwarz inequality.
– Somos
Jul 18 at 17:03