Question

Compute
\[\lim_{n\to\infty}\frac{1}{\sqrt{n}}(1+\frac{1}{\sqrt{2}}+\cdots +\frac{1}{\sqrt{n}})\]

Answer 1

I am not sure about this, but if you expand the bracket than every term will tend to 0 so there sum should tend to 0 too.

Answer 2

1/sqrtn tends to 0, but the sum diverges on its own, so this is why I am not sure

Answer 3

So? what is the answer?