**Question:**

*True/False?*

The series \(1-\frac{1}{\sqrt2}+\frac{1}{\sqrt3}-\frac{1}{\sqrt4}+…\) is divergent.

*Hint:*

Recall the alternating series test (or the Leibniz test)

**Discussion:**

Let \(a_n=\frac{1}{\sqrt{n}}\). The alternating series test says that if we have a series like \(a_1-a_2+a_3-a_4+…\) then a sufficient condition for the convergence of this series is: **\(a_n\) is decreasing and \(a_n\to 0 \) as \(n\to \infty \)**.

Here, \(a_n\) satisfies the above condition.

Therefore, the series converges.

*Related*