Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-$$20 + 10 + 5 + \cdots$$
A) Converges; 40
B) Converges; 20
C) Converges; $- 20$
D) Converges; 35

Question

Quizplus · Accepted Answer

The series is a geometric series with the first term $a = 20$ and common ratio $r = \frac{1}{2}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, so substituting $a = 20$ and $r = \frac{1}{2}$ gives $S = \frac{20}{1 - \frac{1}{2}} = \frac{20}{\frac{1}{2}} = 40$.

Determine Whether the Infinite Geometric Series Converges or Diverges 20+10+5+⋯20 + 10 + 5 + \cdots20+10+5+⋯

Determine Whether the Infinite Geometric Series Converges or Diverges $20 + 10 + 5 + \cdots$