Find the sum of the following infinite geometric series.
$$- 10 + 9 - \frac { 81 } { 10 } + \frac { 729 } { 100 } - \ldots$$
A) $- \frac { 19 } { 100 }$
B) $- \frac { 1 } { 100 }$
C) $\frac { 19 } { 100 }$
D) $- 10$
E) $- \frac { 100 } { 19 }$

Question

Quizplus · Accepted Answer

The series is an infinite geometric series with the first term $a = -10$ and common ratio $r = -\frac{9}{10}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $|r| < 1$. Substituting the given values, we get $S = \frac{-10}{1 - (-\frac{9}{10})} = \frac{-10}{1 + \frac{9}{10}} = \frac{-10}{\frac{19}{10}} = - \frac{100}{19}$.

Find the Sum of the Following Infinite Geometric Series −10+9−8110+729100−…- 10 + 9 - \frac { 81 } { 10 } + \frac { 729 } { 100 } - \ldots−10+9−1081​+100729​−…

Find the Sum of the Following Infinite Geometric Series $- 10 + 9 - \frac { 81 } { 10 } + \frac { 729 } { 100 } - \ldots$