How would you solve for the sum of a series from n=1 to infinity of (5^nx^(2n))/(6^(n+1))

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How would you solve for the sum of a series from n=1 to infinity of (5^nx^(2n))/(6^(n+1))

[From: ] [author: ] [Date: 11-04-29] [Hit: ]

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I have an exam tomorrow and I am not quite sure how to solve this type of problem. An explanation would be really helpful.

Thank you!

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Note that this may be rewritten as Σ(n=0 to ∞) (1/6) * (5x^2/6)^n
= (1/6) * Σ(n=0 to ∞) (5x^2/6)^n, a geometric series.

If |5x^2/6| < 1, then this series converges to (1/6) * 1/(1 - 5x^2/6)) = 1/(6 - 5x^2).

I hope this helps!

1

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