Evaluate the series, if it converges.
-$$10 + 4 + \frac { 8 } { 5 } + \frac { 16 } { 25 } + \ldots$$
A) $\frac { 5 } { 3 }$
B) $\frac { 50 } { 3 }$
C) Does not converge
D) $\frac { 20 } { 3 }$

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = 10$ and common ratio $r = \frac{4}{10} = \frac{2}{5}$. A geometric series converges if $|r| < 1$, which is true in this case. The sum of a convergent geometric series is given by $S = \frac{a}{1 - r}$. Substituting $a = 10$ and $r = \frac{2}{5}$, we get $S = \frac{10}{1 - \frac{2}{5}} = \frac{10}{\frac{3}{5}} = \frac{10 \times 5}{3} = \frac{50}{3}$.

Evaluate the Series, If It Converges 10+4+85+1625+…10 + 4 + \frac { 8 } { 5 } + \frac { 16 } { 25 } + \ldots10+4+58​+2516​+…

Evaluate the Series, If It Converges $10 + 4 + \frac { 8 } { 5 } + \frac { 16 } { 25 } + \ldots$