Question

Find the radius of convergence \[\sum_{1}^{\infty}\left( n \left( x +1 \right)^{n} \right)\div \left( 4^{n} \right)\]

Answer 1

\[-1<(x+1)/4<1\]\[-4<x+1<4\]\[-5<x<3\]

Answer 2

?

Answer 3

that's the radius of convergence