+367 Evaluate the infinite geometric series:
\(2+\frac{1}{9}+\frac{1}{162}+\frac{1}{2916}+\dots\)
Thank You
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
+506 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:
\(\frac{2}{1-\frac{1}{18}} = \frac{2}{\frac{17}{18}} = \frac{36}{17}\)
