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Question

State the following. The Test for Divergence

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Answered 1 year ago

The Test for Divergence states that: If $\lim_{n \rightarrow \infty}{a_n} \ne 0$, then the series $\sum a_n$ diverges. It is also known as the $n$th-term Test. The equivalent form of the statement is: If the series $\sum a_n$ converges, then $\lim_{n \rightarrow \infty}{a_n} = 0$.

Answered 1 year ago

Step 1

1 of 2$\textbf{The Test for Divergence}$

(Also known as the Divergence Test or the $n$-th term Test)

The infinite series $\sum a_n$ is divergent if $\lim\limits_{n \to \infty}a_n=0$ is NOT true.

Answered 1 year ago

Step 1

1 of 2$\textbf{The Test for Divergence:}$

If $\lim a_n \neq 0$, then the series $\sum a_n$ is divergent.

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