 #1
 1,776
 169
 Homework Statement:

If ##\lim_{n\rightarrow \infty} (n . a_n) = 2## , then ##\sum_{n=1}^\infty a_n## diverges.
True of false?
 Relevant Equations:
 not sure
I think ##\lim_{n\rightarrow \infty} a_n = 0## since by direct substitution the value of limit won't be equal to 2 so by direct substitution we must get indeterminate form.
Then how to check for ##\sum_{n=1}^\infty a_n##? I don't think divergence test, integral test, comparison test, limit comparison test, ratio test and root test can be used.
Thanks
Then how to check for ##\sum_{n=1}^\infty a_n##? I don't think divergence test, integral test, comparison test, limit comparison test, ratio test and root test can be used.
Thanks