Question

Find the sum of n terms of the series $3.4+8.11+15.20+24.31+35.44+....$

Answer 1

$\Rightarrow 381524\mathrm{35....}$

$579\mathrm{11....}$

$22\mathrm{2....}$

$u_n=n^2+2n$

$4112031\mathrm{44....}$

$7911\mathrm{13....}$

$22\mathrm{2....}$

$u_n=n^2+4n-1$

$\therefore t_n=(n^2+2n)(n^2+4n-1)$

$=n(n+2)((n+1)(n+3)-4)$

$=n(n+1)(n+2)(n+3)-4n(n+2)$

$S_n=\frac{n(n+1)(n+2)(n+3)(n+4)}{5}-\frac{4n(n+1)(n+2)}{3}-2n(n+1)$

$=\frac{n(n+1)}{15}(3n^2+27n^2+58n+2)$