Question

calculate the sum of the following series if possible, or explain why the series diverges
inf sigma n=1 ((6^(n+1)+5^n)/7^n)

Answer 1

\[\sum_{n=1}^{\infty} ((6^{n+1}+5^{n})/7^{n})\]

Answer 2

\[\sum_{k=1}^{\infty}((6^{k+1}+5^k)/7^k)=\sum_{k=1}^{\infty}\frac{6^{k+1}}{7^k}+\sum_{k=1}^{\infty}\frac{5^k}{7^k}\]\[=6\sum_{k=1}^{\infty}(\frac{6}{7})^k+\sum_{k=1}^{\infty}(\frac{5}{7})^k\]

Answer 3

Use your formula for the sum of this kind of series to find the numbers.

Answer 4

As I recall, \[\sum_{k=0}^{\infty}x^k=\frac{1}{1-x}~~~~|x|<1\]

Answer 5

Make sure you take the zeroeth term that is missing from the problem, but present in the formula.