Find the infinite sum accurate to three decimal places.
-$$\sum _ { n = 1 } ^ { \infty } \frac { 2 ( - 1 ) ^ { n + 1 } } { 3 ^ { n } }$$
A) 1.500
B) 3.000
C) 0.500
D) 1.000

Question

Quizplus · Accepted Answer

The given infinite series is an alternating geometric series with first term $a=2/3$ and common ratio $r=-1/3$. Thus we can use the formula for the sum of an infinite geometric series:
$$S=\frac{a}{1-r}=\frac{2/3}{1+1/3}=\frac{2}{4/3}=0.5$$
Thus the answer is (C).

Find the Infinite Sum Accurate to Three Decimal Places ∑n=1∞2(−1)n+13n\sum _ { n = 1 } ^ { \infty } \frac { 2 ( - 1 ) ^ { n + 1 } } { 3 ^ { n } }n=1∑∞​3n2(−1)n+1​

Find the Infinite Sum Accurate to Three Decimal Places $\sum _ { n = 1 } ^ { \infty } \frac { 2 ( - 1 ) ^ { n + 1 } } { 3 ^ { n } }$