Question says: [itex]\sum(cos(n*pi)/5^n)[/itex] from 0 to infinity.(adsbygoogle = window.adsbygoogle || []).push({});

Proved that it converges: ratio test goes to abs(cos(pi*(n+1))/5cos(pi*n)) with some basic algebra. As n goes to infinity, this approaches -1/5 (absolute value giving 1/5) since cos(pi*(n+1))/cos(pi*n) is always -1, excepting the asymptotes.

Question wants to find sum. Wolfram claims sum is 5/6 and won't elaborate. How?

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# Homework Help: Infinite series

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