+0

0
46
2
+312

Evaluate the infinite geometric series:

$$2+\frac{1}{9}+\frac{1}{162}+\frac{1}{2916}+\dots$$

Thank You

Dec 28, 2020

#1
+1

Common ratio    2 * r = 1/9         r = 1/18

sum = a1 (1-r^n)/(1-r)

= a1(1/(1-r) ) =   2 (1/(1-1/18)) = 2.12

Dec 28, 2020
#2
+66
+3

The common ratio between 2 terms in this geometric series is 1/18, and the first term of this geometric series is 2.

The sum of an infinite geometric series, if the common ratio is strictly greater than -1 and less than 1 and not equal to zero, is equal to $$a\over(1-r)$$, where "a" is the first term and "r" is the common ratio.

Therefore, the answer to this is:

$$\frac{2}{1-\frac{1}{18}} = \frac{2}{\frac{17}{18}} = \frac{36}{17}$$

Dec 28, 2020