proof-or-given-a-counter-example-for-s-2-3-4-5-i-1-n-1-s-i-1-i-i-s-i-1-n-s-1-si-s-

Question Number 480 by 123456 last updated on 11/Jan/15

p r o o f o r g i v e n a c o u n t e r e x a m p l e :

f o r s \in {2, 3, 4, 5}

\underset{i = 1}{\sum^{n}} [\frac{1}{s^{i}} - \frac{{(- 1)}^{i}}{i^{s}}] ⩽ \underset{i = 1}{\sum^{n}} \frac{s + 1}{{s i}^{s}}

Commented by prakash jain last updated on 13/Jan/15

First counter example only at s = 7 .

Which is not in the given set .