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**gilyos** $\displaystyle b_{n} = 1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\f rac{!}{n^2}$

a) Prove that this series have limit b ,

b) prove that the limit b , hold $\displaystyle \frac{49}{36} < b < 2$

I start to solve :

$\displaystyle \frac{1}{n^2} < \frac{1}{n(n-1)} = \frac {1}{n-1} - \frac{1}{n}$

so

$\displaystyle b_{n} = 1 + \frac{1}{1}-\frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... \frac{1}{n-1} - \frac{1}{n} = 2 - \frac{1}{n} < 2$

How I prove that the series rise ?

and how I prove b)