Proving the ratio test fails.

**cgiulz** · October 12th 2009, 04:27 PM

Can anyone prove that the ratio test is inconclusive when

$\lim_{n \rightarrow \infty} |\frac{a_{n+1}}{a_{n}}| = 1,$ or

$\lim_{n \rightarrow \infty} |\frac{a_{n+1}}{a_{n}}| DNE.$

**Jose27** · October 12th 2009, 04:31 PM

For the first one take $a_n= \frac{1}{n}$ and $b_n= \frac{1}{n^2}$ both limits are 1, but one converges and the other diverges. For the second I'm not sure...

Thread: Proving the ratio test fails.

LinkBack

Thread Tools

Display

Proving the ratio test fails.

Similar Math Help Forum Discussions

Classifying Critical Points when 2nd Derivative test FAILS

Determining the type of critical point when the second derivative test fails

Proving the Ratio Test

Help testing these series with any root test or ratio test.

ratio test (series) urgent test tommorow!

Search Tags