Question

40 POINTS!!

Find the sum of n terms of the series. 
$( {n}^{2} - {1}^{2} ) + 2( {n}^{2} - {2}^{2} ) + 3( {n}^{2} - 3^{2})......$
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Answer 1

Answer

1/4[n^2(n^2 - 1)]

Step-by-step explanation:

By removing the brackets

n^2[1+2+3+..... +n] - [1+9+27+....+n^3]

= n^3(n+1)/2 - [n(n+1)]^2/4

= n^2(n + 1) (2n-n-1)/4

= 1/4[n^2(n^2 - 1)]