Question Number 480 by 123456 last updated on 11/Jan/15
![proof or given a counter example: for s∈{2,3,4,5} Σ_(i=1) ^n [(1/s^i )−(((−1)^i )/i^s )]≤Σ_(i=1) ^n ((s+1)/(si^s ))](Q480.png)
$${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${for}\:{s}\in\left\{\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[\frac{\mathrm{1}}{{s}^{{i}} }−\frac{\left(−\mathrm{1}\right)^{{i}} }{{i}^{{s}} }\right]\leqslant\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{s}+\mathrm{1}}{{si}^{{s}} } \\ $$
Commented by prakash jain last updated on 13/Jan/15
$$\mathrm{First}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{only}\:\mathrm{at}\:{s}=\mathrm{7}. \\ $$$$\mathrm{Which}\:\mathrm{is}\:\mathrm{not}\:\mathrm{in}\:\mathrm{the}\:\mathrm{given}\:\mathrm{set}. \\ $$