# calculus 2 help?

Determine if the series converges or diverges. If it converges, find its sum:

∞

Σ 2/(n^2 + 2n)

n=3

### 2 Answers

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- Wayne DeguManLv 72 months ago
2/(n² + 2n) => 2/[n(n + 2)]

i.e. (1/n) - 1/(n + 2)

Using n = 3, 4, 5, 6,...we get:

1/3 - 1/5

1/4 - 1/6

1/5 - 1/7

1/6 - 1/8

1/7 - 1/9....e.t.c.

Terms cancel apart from 1/3 + 1/4 - 1/(n + 1) - 1/(n + 2)

As n --> ∞, 1/(n + 1) and 1/(n + 2) --> 0

so, sequence tends to a limit of 1/3 + 1/4

i.e. sum to infinity is 7/12

- 2 months ago
here is a hint rewrite the expression as 1/n - 1/ (n+2) and I think you will get it

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