We have to find the sum of the terms An = n^2 + 12n
Now Sum [ An], of n terms
=> Sum [ n^2 + 12n ] , of n terms
=> Sum [ n^2] + Sum [ 12n] , of n terms
=> n(n+1)(2n+1)/6 + 12* n(n+1)/2
=>...
See This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Already a member? Log in here.
We have to find the sum of the terms An = n^2 + 12n
Now Sum [ An], of n terms
=> Sum [ n^2 + 12n ] , of n terms
=> Sum [ n^2] + Sum [ 12n] , of n terms
=> n(n+1)(2n+1)/6 + 12* n(n+1)/2
=> n(n+1)(2n+1)/6 + 6*n(n+1)
=> n(n+1) [ (2n+1)/6 + 6]
=> n(n+1)[ (2n + 1 + 36)/6)]
=> n(n+1)(2n + 37)/ 6
=> (1/6)*n*(n+1)*(2n+ 37)
The required sum is (1/6)*n*(n+1)*(2n+ 37)