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 $\displaystyle \left(-1\right)^n$ term, you should always first start off with the alternating series test.
The absolute value leaves us with $\displaystyle 2^{\frac1n}$
Since $\displaystyle 2^{\frac1n}>2^{\frac1{n+1}}$, we need to see if $\displaystyle \lim\left|s_n\right|=0$. However, $\displaystyle \lim\left|s_n\right|=\lim 2^{\frac1n}=1\neq0$.
Thus, it diverges.