calculus 2 help?

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

Σ          2/(n^2 + 2n)

n=3

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  • 2 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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