If $\sum a_{k}$ is the sum of a series of numbers and $\lim _{k \rightarrow \infty} \alpha_{k}=0$ , then the series converges.

Question

Quizplus · Accepted Answer

The condition $\lim _{k \rightarrow \infty} a_{k}=0$ is necessary but not sufficient for the convergence of the series $\sum a_{k}$. A series can diverge even if its terms approach zero. For example, the harmonic series $\sum \frac{1}{n}$ diverges even though $\lim _{n \rightarrow \infty} \frac{1}{n} = 0$.

If ∑ak\sum a_{k}∑ak​ Is the Sum of a Series of Numbers And

If $\sum a_{k}$ Is the Sum of a Series of Numbers And