Question

Calculus Problem!!
Decide whether each of the following series converges. If a given series converges, find its sum.
sum_{n=1}^{infty}(sin (-2n)-sin (-2(n+1)))
sum_{n=1}^{infty}(e ^{10n}-e ^{10(n+1)})
sum_{n=1}^{infty}(sin(-2/n)-sin(-2/(n+1)))

Answer 1

damn ... can see a thing .. latex problem

Answer 2

looks like first one neither converges or diverges, since it is an oscillating series,
the second diverges,
the third converges

Answer 3

∑(bottom:n=1,upper:∞) (sin(−2n)−sin(−2(n+1)))
∑(bottom:n=1,upper:∞) (e^(10n)−e^(10(n+1)))
∑(bottom:n=1,upper:∞) (sin(−2/n)−sin(−2/(n+1)))

Answer 4

let's use sin c - sin d formula

Answer 5

1) gives you cos 2n which is again an oscillating seq ... neither conv nor div
2) second div .. just split that ex
3) ... try that later