Question

Find `sum_1^7 (1+n^2)`?

Answer 1

`sum_1^7 (1+n^2)=147`

Explanation:

`sum_1^7 (1+n^2)=7+sum_1^7 n^2`

Using the identity `sum_1^n n^2=(n(n+1)(2n+1))/6`

Hence `sum_1^7 n^2=(7(7+1)(2xx7+1))/6`

`=(7xx8xx15)/6=140`

Hence `sum_1^7 (1+n^2)=147`

Check - `sum_1^7 (1+n^2)=2+5+10+17+26+37+50=147`