_ n (1²+2²+ +n² ) [n] n (n+1)(n+10)(n+100) =

Step-by-step solution

We have, aligned _ n (1²+2²+ +n² ) [n] n (n+1)(n+10)(n+100) =& _ n n(n+1)(2 n+n) 6(n+1)(n+10)(n+100) ( _ n [n] n ) =& _ n 2 n²+n 6(n+10)(n+100) =& _ n 2+ 1 n 6 (1+ 10 n ) (1+ 100 n ) =& 2+0 6(1+0)(1+0) =& 2 6 = 1 3 aligned