Determine the sum of the series $1 + \frac { 1 } { 1.01 } + \frac { 1 } { ( 1.01 ) ^ { 2 } } + \frac { 1 } { ( 1.01 ) ^ { 3 } } + \ldots$
A) 101
B) $\frac { 1 } { 1.01 }$
C) 10.1
D) none of these

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = 1$ and common ratio $r = \frac{1}{1.01}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $|r| < 1$. Substituting the given values, we get $S = \frac{1}{1 - \frac{1}{1.01}} = \frac{1}{\frac{0.01}{1.01}} = \frac{1.01}{0.01} = 101$.

Determine the Sum of the Series 1+11.01+1(1.01)2+1(1.01)3+…1 + \frac { 1 } { 1.01 } + \frac { 1 } { ( 1.01 ) ^ { 2 } } + \frac { 1 } { ( 1.01 ) ^ { 3 } } + \ldots1+1.011​+(1.01)21​+(1.01)31​+…

Determine the Sum of the Series $1 + \frac { 1 } { 1.01 } + \frac { 1 } { ( 1.01 ) ^ { 2 } } + \frac { 1 } { ( 1.01 ) ^ { 3 } } + \ldots$