Evaluate the series, if it converges.
-$$\sum _ { i = 1 } ^ { \infty } 25 \left( \frac { 7 } { 10 } \right) ^ { i - 1 }$$
A) $\frac { 250 } { 3 }$
B) $\frac { 175 } { 3 }$
C) Does not converge.
D) $\frac { 10 } { 3 }$

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = 25$ and common ratio $r = \frac{7}{10}$. The sum of a convergent geometric series is given by $S = \frac{a}{1 - r}$. Substituting $a = 25$ and $r = \frac{7}{10}$, we get $S = \frac{25}{1 - \frac{7}{10}} = \frac{25}{\frac{3}{10}} = \frac{250}{3}$.

Evaluate the Series, If It Converges ∑i=1∞25(710)i−1\sum _ { i = 1 } ^ { \infty } 25 \left( \frac { 7 } { 10 } \right) ^ { i - 1 }i=1∑∞​25(107​)i−1

Evaluate the Series, If It Converges $\sum _ { i = 1 } ^ { \infty } 25 \left( \frac { 7 } { 10 } \right) ^ { i - 1 }$