CBSE Class 11-science Answered

7. 12 + (12 + 22) + (12 + 22 + 32) + ...  =  [7. 12 ]+ (12 + 22) + (12 + 22 + 32) + ...

The firsr term is = 84. Now look at the terms starting from the second   (12 + 22) + (12 + 22 + 32) + ...

The general term will be sum of AP with a = 12 and d = 10. i,e n/ 2 [ 2 x 12 + ( n-1) 10]  = 7n + 5 n²

  7n + 5 n²  =  is the sum of the given series from second term onwards . I presume  it is till (n+1) the terms

 so 7 n (n+1) / 2 + 5n (n+1) (2n +1) / 6  = n(n+1) / 2 [ 7 + 5(2n +1) /3 ]

=n(n+1) / 2[26+10n] / 6

So 7. 12 + (12 + 22) + (12 + 22 + 32) + ...  = 84 + n(n+1) [13+5n] / 6