Question

Sigma Notation Write the sum using sigma notation.

$1^2+2^2+3^2+\mathrm{....}+{10}^2$

Short answer

The sum using sigma notation is$\sum _{n=1}^{10}{n}^2.$

Step-by-step solution

Step 1.  Given

The given sequence is$1^2+2^2+3^2+\mathrm{....}+{10}^2$.

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 n.

It is easy to see from the given sequence that the nth term is $n^2$.

And n goes from 1 to 10.

Hence, the sum is given by: $\sum _{n=1}^{10}{n}^2$.