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?

Question

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?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

answer is 3/8

anonymous · Answer

attachment