Science:Math Exam Resources/Courses/MATH101/April 2015/Question 02 (c) (iii)/Solution 1

Let $a_{n}=(-1)^{n}n$. Obviously, $a_{n}$ doesn't converges to 0.

Indeed, if we assume $a_{n}$ converges to 0, then $|a_{n}|=n$ also converges to 0, which is a contradiction. $\left(\because \lim _{n\to \infty }n=+\infty .\right)$

Therefore, by the divergence test, the given summation diverges.

The answer: DT