test for the series for convergence or divergence 3

**twilightstr** · April 5th 2009, 08:36 PM

determine if series is convergent or divergent
the sum from 1 to infinity of (-1)^n(2^(1/n))

**Chris L T521** · April 5th 2009, 09:04 PM

Originally Posted by twilightstr

determine if series is convergent or divergent
the sum from 1 to infinity of (-1)^n(2^(1/n))

Its somewhat similar to your other problem here.

Whenever you have a $\left(-1\right)^n$ term, you should always first start off with the alternating series test.

The absolute value leaves us with $2^{\frac1n}$

Since $2^{\frac1n}>2^{\frac1{n+1}}$ , we need to see if $\lim\left|s_n\right|=0$ . However, $\lim\left|s_n\right|=\lim 2^{\frac1n}=1\neq0$ .

Thus, it diverges.

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