Prove that 1 + (1/4) + (1/9) + …+ (1/n^2 )


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Question Number 159497 by naka3546 last updated on 17/Nov/21

$P r o v e t h a t$ $1 + \frac{1}{4} + \frac{1}{9} + \dots + \frac{1}{n^{2}} < 2$ $f o r n \in N .$
Commented by mr W last updated on 18/Nov/21

$1 + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . + \frac{1}{n^{2}}$ $< 1 + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . + \frac{1}{n^{2}} + \frac{1}{{(n + 1)}^{2}} + . . . = \frac{π^{2}}{6}$ $< \frac{10}{6} < \frac{12}{6} = 2$ $\Rightarrow 1 + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . + \frac{1}{n^{2}} < 2$
Commented by naka3546 last updated on 18/Nov/21

$T h a n k y o u, s i r .$
Commented by SANOGO last updated on 18/Nov/21

$p r k w \frac{π^{2}}{6} e x p l i q u e m o i u n p e u$
Commented by mr W last updated on 18/Nov/21
https://en.m.wikipedia.org/wiki/Basel_problem
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