Use Theorem 9.11 to determine the convergence or divergence of the series. $\sum _ { n = 1 } ^ { \infty } \frac { 2 } { \frac { 5 } { 9 } }$
A) converges
B) diverges
C) Theorem 9.11 inconclusive

Question

Quizplus · Accepted Answer

Theorem 9.11 states that a series of the form $\sum_{n=1}^\infty \frac{1}{a_n}$ converges if and only if the sequence $\{a_n\}$ diverges to infinity. In this case, $\frac{5}{9}$ is a constant, so the sequence $\{\frac{5}{9}\}$ does not diverge to infinity. Therefore, the series diverges by Theorem 9.11. The correct choice is (B).

Use Theorem 9 ∑n=1∞259\sum _ { n = 1 } ^ { \infty } \frac { 2 } { \frac { 5 } { 9 } }∑n=1∞​95​2​

Use Theorem 9 $\sum _ { n = 1 } ^ { \infty } \frac { 2 } { \frac { 5 } { 9 } }$