Question

How do you find the sum of 1/(8^n) from n=1 to infinity? I know it equals 8/49 but I don't know how/why

Answer 1

\[\sum_{n=1}^{+\infty}\frac{1}{8^n}=\frac{1}{8}+\frac{1}{8^2}+\frac{1}{8^3}+\cdots
=\frac{1}{8}\cdot\frac{1}{1-1/8}=\frac{1}{7}\]

Answer 2

sorry i meant the sum of n/8^n

Answer 3

8/49

Answer 4

thank you :)