Determine the convergence or divergence of the series. $\sum _ { n = 0 } ^ { \infty } \left( \frac { 3 } { 10 } \right) ^ { n }$
A)inconclusive
B)diverges
C)converges

Question

Quizplus · Accepted Answer

This series is a geometric series with a common ratio $r = \frac{3}{10}$, which is between -1 and 1 ($-1 < r < 1$). According to the geometric series convergence test, a geometric series converges if and only if the absolute value of the common ratio is less than 1. Since $|r| = \left|\frac{3}{10}\right| = 0.3 < 1$, the series converges.

Determine the Convergence or Divergence of the Series ∑n=0∞(310)n\sum _ { n = 0 } ^ { \infty } \left( \frac { 3 } { 10 } \right) ^ { n }∑n=0∞​(103​)n

Determine the Convergence or Divergence of the Series $\sum _ { n = 0 } ^ { \infty } \left( \frac { 3 } { 10 } \right) ^ { n }$