Question

How do you find the sum of the series `n^2` from n=1 to 6?

Answer 1

`91`

Explanation:

Adding the individual terms in the sum.

`sum_(n=1)^6n^2`

`=1^2+2^2+3^2+4^2+5^2+6^2`

`=91`

`color(blue)"OR"`

`color(red)"Knowledge of the summation identity"`

`sum_(n=1)^6n^2=1/6n(n+1)(2n+1)`

Using n = 6

`=1/6xx6(6+1)(12+1)=1xx7xx13`

`=91`