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- Mar 12th 2010, 11:00 AMkingwinnerRoot test & Ratio test
- Mar 12th 2010, 11:12 AMadam63
Ratio test : first of all, if $\displaystyle \frac{a_{k+1}}{a_k} \rightarrow \infty$, then the sequence does not converge, which means the series $\displaystyle \sum a_k$ surely won't converge.

Same with the root test - if limsup$\displaystyle (a_k)^\frac{1}{k} \rightarrow \infty$, then $\displaystyle a_k \rightarrow \infty$, and the sequence diverges, so the series will diverge too. - Mar 13th 2010, 03:52 PMkingwinner
- Mar 14th 2010, 03:31 AMadam63
a series can converge ONLY if the sequence converges.

Then, if the sequence diverges, the series will surely diverge :) .