PROBLEM NO.33(B0MC-2,DAY-5)
Posted: Thu Apr 05, 2012 12:37 am
For every positive integer $n$,prove that
\[\sum _{i=1}^{n}\frac{\sigma (i)}{i}\leqslant 2n \].
\[\sum _{i=1}^{n}\frac{\sigma (i)}{i}\leqslant 2n \].
(i)
\[\sum _{d|n}\frac{1}{d}= \frac{\sigma (n)}{n}\]
Try to show that \[\sum _{k=1}^{n}\frac{1}{k^{2}}< 2\]