# Converging or Diverging...??

• Jan 28th 2009, 07:42 PM
Angel Rox
Converging or Diverging...??
Determine whether the series: $\sum_{n=1}^\infty$ 25^-n+2 . 16^n+1converges or diverges. If it converges then find its sum

Can I have some hints in solving this question..(Doh)
• Jan 28th 2009, 09:07 PM
mr fantastic
Quote:

Originally Posted by Angel Rox
Determine whether the series: $\sum_{n=1}^\infty$ 25^-n+2 . 16^n+1converges or diverges. If it converges then find its sum

Can I have some hints in solving this question..(Doh)

Two hints:

1. $25^{-(n+2)} \cdot 16^{n+1} = \frac{16^{n+1}}{25^{n+2}} = \frac{16}{25^2} \cdot \left( \frac{16}{25} \right)^n$.

2. Sum of an infinite geometric series.