Question

How can show that the sum converges absolutely?

Answer 1

\[\sum_{n=1}^{∞}\frac{ (-1)n^2+3n+7 }{ 2^n+1 }\]

Answer 2

The absolute value of \((−1)n^2+3n+7\) is always smaller (bad bound but suffices) 3n^2 . Also, 2n−1 is bigger than \(2^{n-1}\).
Show that \(∑_{n=1}\frac{3n^2}{2^{n-1}}\) converges. and finally use the comparison criterion.

Answer 3

err: \(2^{n}-1\) is bigger than \(2^{n-1}\)