Determining convergence/divergence of infinite series

[cpm3b]

I am having trouble determining the convergence(absolutely or conditionally)/divergence of these two series.

1) the summation of ((n+1)((10^2)-1)^n)/(10^(2n)) from n=1 to infinity

and

2) the summation of ((-3)^n)/(n^3) from n=1 to infinity

Which tests should I use and how do i go about differentiating between absolutely convergent and conditionally convergent series?

 

[pka]

\(\displaystyle \frac{{\left( {10^2 - 1} \right)^n }}{{10^{2n} }} = \frac{{\left( {99} \right)^n }}{{\left( {100} \right)^n }} = \left( {.99} \right)^n \Rightarrow \quad \sum\limits_{n = 1}^\infty {\left( {n + 1} \right)\left( {.99} \right)^n }\)

On #2 use the root test of the absolute value: \(\displaystyle \sqrt[n]{{\frac{{3^n }}{{n^3 }}}}\)