Calculus
posted by Isaac
How can I prove this series alternating series converges(this is the answer)?
(1)^2*(2/3)^n
I tried it this way: an = (2/3)^n, then i just broke it down. 2^n/(3^n) and i took the ratio of it and got 2/3 which does not equal to one which would mean the series diverges.. but that's obviously not how its done i guess

Steve
I assume you mean
(1)^n * (2/3)^n
This is just a geometric series with r = 2/3
So, if you start with n=0, the sequence starts with 1, and
Sum = 1/(1r) = 1/(1+2/3) = 3/5
In an alternating series, if the ratio r < 1 it converges.
Respond to this Question
Similar Questions

Calculus
If you have a geometric alternating series, and you prove that the series is converging by doing geometric series test, and NOT alternating series test, then does that allow you to say that the series converges ABSOLUTELY? 
Calc
Does 1/ln(x+1) converge or diverge? I've tried the nth term test, limit comparison test, and integral test. All I get is inconclusive. The other tests I have (geometric series, pseries, telescoping series, alternating series, and 
calculus
test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (1)^n/(3n+1) I said it converges, is this true? 
calculus
test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (1)^n/(3n+1) I said it converges, is this true? 
Calculus
a) Find the Taylor series associated to f(x) = x^2 at a = 1. Be sure to show the general term of the series. b) Find the radius of convergence of the series. c)Use Lagrange's Remainder Theorem to prove that for x in the interval of … 
Calculus
Determine the following about the series. Indicate the test that was used and justify your answer. Sigma (lower index n = 1; upper index infinity) [sin((2n1)pi/2)]/n A. The series diverges B. The series converges conditionally. C. … 
Integral Calculus
We can use this power series to approximate the constant pi: arctan(x) = (summation from n = 1 to infinity) of ((1)^n * x^(2n+1))/(2n+1) a) First evaluate arctan(1) without the given series. (I know this is pi/4) b) Use your answer … 
Calculus
The divergence test applied to the series ∑n=1 to ∞ 3n/(8n+9) tells us that the series converges or diverges? 
Calculus
Use the ratio test to find whether the series diverges or converges. 1/5^n (1 to infinity) I think the limit converges to 1/5, so the series converges. 
Calculus
Determine whether the series from 0 to infinity of cos(nπ)/(n + 3) converges conditionally or absolutely. A. The series diverges. B. The series converges conditionally but not absolutely. C. The series converges absolutely but not …