Question

Sigma Notation Write the sum using sigma notation.

$\frac{\sqrt{1}}{1^2}+\frac{\sqrt{2}}{2^2}+\frac{\sqrt{3}}{3^2}+\mathrm{....}+\frac{\sqrt{n}}{n^2}$

Short answer

The sum using sigma notation is$\sum _{k=1}^n\frac{\sqrt{k}}{k^2}.$

Step-by-step solution

Step 1.  Given

The given sequence is$\frac{\sqrt{1}}{1^2}+\frac{\sqrt{2}}{2^2}+\frac{\sqrt{3}}{3^2}+\mathrm{....}+\frac{\sqrt{n}}{n^2}.$

Step 2.  To determine

We have to write the sum using sigma notation.

Step 3.  Calculation

We try to write the given sequence using a general term with k.

From the given sequence it is easy to see that the kth term is $\frac{\sqrt{k}}{k^2}$.

And k goes from 1 to n.

Hence, the sum is given by: $\sum _{k=1}^n\frac{\sqrt{k}}{k^2}$.