Evaluate the series, if it converges.
-$$\sum _ { i = 1 } ^ { \infty } 46 \left( - \frac { 5 } { 7 } \right) ^ { i - 1 }$$
A) Does not converge.
B) $- \frac { 115 } { 6 }$
C) $\frac { 7 } { 12 }$
D) $\frac { 161 } { 6 }$

Question

Quizplus · Accepted Answer

The series is a geometric series with first term $a = 46$ and common ratio $r = -\frac{5}{7}$. Since $|r| < 1$, the series converges to $\frac{a}{1-r} = \frac{46}{1 - (-\frac{5}{7})} = \frac{46}{1 + \frac{5}{7}} = \frac{46}{\frac{12}{7}} = \frac{46 \times 7}{12} = \frac{322}{12} = \frac{161}{6}$.

Evaluate the Series, If It Converges ∑i=1∞46(−57)i−1\sum _ { i = 1 } ^ { \infty } 46 \left( - \frac { 5 } { 7 } \right) ^ { i - 1 }i=1∑∞​46(−75​)i−1

Evaluate the Series, If It Converges $\sum _ { i = 1 } ^ { \infty } 46 \left( - \frac { 5 } { 7 } \right) ^ { i - 1 }$