calculus
posted by laura
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?

rich
Hi:
You are correct. The test criteria are,
1) The terms a_n are of decreasing sequence; clearly 1/(3n+1) is decreasing on [1, inf].
2) Limit(n>inf)[a_n] = 0.
Both criteria having been met, we conclude convergence.
Regards,
Rich B. 
Dan
"If the sequence An converges to 0, and each An is smaller than An1 (i.e. the sequence An is monotone decreasing), then the series converges."
In this case, An = 1 / (3n + 1)
The limit as n>infinity (An) = 0
A1 = 1 / 4
A2 = 1 / 7
Therefore, by the Alternating Series Test the series converges.
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