Question

Find the sum of the series.

∑(n = 0, ∞) 2/9^n

Answer 1

\[\sum_{n=0}^\infty \left(\frac{2}{9}\right)^n~~\text{or}~~\sum_{n=0}^\infty\frac{2}{9^n}~~?\]

Answer 2

the second!

Answer 3

Recall the formula:
\[\sum_{n=0}^\infty ar^n=\frac{a}{1-r}\]
You can write your series to match this formula to easily evaluate the sum:
\[\sum_{n=0}^\infty 2\left(\frac{1}{9}\right)^n=\frac{2}{1-\frac{1}{9}}=\frac{9}{4}\]

Answer 4

This is very helpful, thank you!!

Answer 5

yw