Asked by Anonymous
Which of the following series converge?
A. 1 + 1/2^2 + 1/3^2 + ... + 1/n^2 + ...
B. 1 + 1/2 + 1/3 + ... + 1/n + ...
C. 1 - 1/3 + 1/3^2 - ... + ((-1)^(n+1))/(3^(n-1)) + ...
I think A and C are the answer.
A. 1 + 1/2^2 + 1/3^2 + ... + 1/n^2 + ...
B. 1 + 1/2 + 1/3 + ... + 1/n + ...
C. 1 - 1/3 + 1/3^2 - ... + ((-1)^(n+1))/(3^(n-1)) + ...
I think A and C are the answer.
Answers
Answered by
Steve
A does, since ∑1/n^p converges for p>1
B does not -- the Harmonic Series
C does, since ∑1/3^n is just a geometric series with r<1
you are correct
B does not -- the Harmonic Series
C does, since ∑1/3^n is just a geometric series with r<1
you are correct
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