- #1
Damidami
- 94
- 0
I read that an alternating series [tex] \Sigma (-1)^n a_n [/tex] converges if "and only if" the sequence [tex]a_n [/tex] is both monotonous and converges to zero.
I tried with this series:
[tex] \Sigma_{n=1}^{\infty} (-1)^n | \frac{1}{n^2} \sin(n)| [/tex]
in the wolfram alpha and seems to converge to -0.61..., even if [tex] a_n = |\frac{1}{n^2} \sin(n)| [/tex] is not monotonous decreasing.
What am I doing wrong? Is the monotone condition necesary for this test, but the fact that a_n is not monotonous does not guarantee if the series converges or not?
Thanks.
I tried with this series:
[tex] \Sigma_{n=1}^{\infty} (-1)^n | \frac{1}{n^2} \sin(n)| [/tex]
in the wolfram alpha and seems to converge to -0.61..., even if [tex] a_n = |\frac{1}{n^2} \sin(n)| [/tex] is not monotonous decreasing.
What am I doing wrong? Is the monotone condition necesary for this test, but the fact that a_n is not monotonous does not guarantee if the series converges or not?
Thanks.