proof or given a counter example: for s∈{2,3,4,5} Σ_(i=1) ^n [(1/s^i )−(((−1)^i )/i^s )]≤Σ


Question and Answers Forum

All Questions Topic List
Geometry Questions
Previous in All Question Next in All Question
Previous in Geometry Next in Geometry
Question Number 480 by 123456 last updated on 11/Jan/15
$proof or given a counter example: for s∈{2,3,4,5} Σ_(i=1) ^n [(1/s^i )−(((−1)^i )/i^s )]≤Σ_(i=1) ^n ((s+1)/(si^s ))$
$p r o o f o r g i v e n a c o u n t e r e x a m p l e :$ $f o r s \in {2, 3, 4, 5}$ $\underset{i = 1}{\sum^{n}} [\frac{1}{s^{i}} - \frac{{(- 1)}^{i}}{i^{s}}] ⩽ \underset{i = 1}{\sum^{n}} \frac{s + 1}{{s i}^{s}}$
Commented by prakash jain last updated on 13/Jan/15

$First counter example only at s = 7 .$ $Which is not in the given set .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum