Question

Find the sum of n terms of the series $1.5+2.15+3.31+4.53+5.81+....$

Answer 1

$\Rightarrow 5153153quad\mathrm{81....}$

$101622\mathrm{28....}$

$66\mathrm{6....}$

$u_n=5+10(n-1)+3(n-1)(n-2)$

$=5+10n-10+3n^2-9n+6$

$=3n^2+n+1$

$\therefore t_n=n(3n^2+n+1)$

$=3n^3+n^2+n$

$S_n=\sum t_n=\frac{3n^2(n+1{)}^2}{4}+\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}$

$=\frac{n(n+1)}{12}(9n^2+13n+8)$