## nestor18 2 years ago What does the series converge to? 3/5-9/25+27/125-....... This is a geometric alternating series where A=3/5 and r=3^n/5^n? I think how would I get to its convergence?

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1. gasgengar

The summation of these geometric series to infinity is = a[(1-R^(n+1))/(1-R)] I assume you know how this answer comes from, so a = 3/5, R = (-1) (3/5) and n tends to infinity you'll get the answer = (3/5)/(1+3/5) = 3/8

2. nestor18

I had a brain fart, series was not my strong suit in Calc 2, we barely touched on it.Thanks

3. cinar

$\Large\sum_{n=1}^{\infty}{(-1)^{n+1}}(\frac{3}{5})^n$

4. nestor18

I originally put the standard A/1-r and got 15/10, but then I noticed it was an alternating series

5. cinar