Geometric Series

Evaluate the geometric Series or state that it diverges

lower bound k= 1 upper bound = infinity

E (sum symbol) E 5(-1/6)^(5k)

I know it converges but im not sure to what

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  1. a = 5(-1/6)^5
    Note that (-1/6)^(5k) = ((-1/6)^5)^k, so
    r = (-1/6)^5

    S = a/(1-r) = (5(-1/6)^5)/(1-(-1/6)^5) = -5/7777

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