let x={(1/n)}_(n=1) ^∞ and y={(1/(n+1))}_(n=1) ^∞ be a sequence of real numbers and l_(2 ) ={x=(x_1 ,x_2 ,x_3 ,...):Σ_(n=1) ^∞ ∣xi∣^2 <∞} a linear space. (1) verify that x and y are in l_2 . (2) compute the inner product of x and y on l


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Question Number 31314 by Abdullai otchere last updated on 08/Mar/18
$let x={(1/n)}_(n=1) ^∞ and y={(1/(n+1))}_(n=1) ^∞ be a sequence of real numbers and l_(2 ) ={x=(x_1 ,x_2 ,x_3 ,...):Σ_(n=1) ^∞ ∣xi∣^2 <∞} a linear space. (1) verify that x and y are in l_2 . (2) compute the inner product of x and y on l_2 please help me solve this question.$
$l e t x = {\frac{1}{n}}_{n = 1}^{\infty} a n d y = {\frac{1}{n + 1}}_{n = 1}^{\infty} b e$ $a s e q u e n c e o f r e a l n u m b e r s a n d$ $l_{2} = {x = (x_{1}, x_{2}, x_{3}, . . .) : \underset{n = 1}{\sum^{\infty}} ∣ x i ∣^{2} < \infty}$ $a l i n e a r s p a c e .$ $(1) v e r i f y t h a t x a n d y a r e i n l_{2} .$ $(2) c o m p u t e t h e i n n e r p r o d u c t o f x$ $a n d y o n l_{2}$ $p l e a s e h e l p m e s o l v e t h i s$ $q u e s t i o n .$
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