# find the sum upto n terms  of the series: (with proper steps)2+4+9+17+28+..........

$\\T_r=t_{r+1}-t_{r} \\t_{r+1}=T_r+t_{r}=T_r+T_{r-1}+t_{r-1}... \\T_r=2+(r-1)3 \\2+(2+T(1))+(2+T(1)+T(2))+(2+T(1)+T(2)+T(3)).... \\=>2*n+\sum_{1}^{n-1}\sum{T_r} \\=>2*n+\sum_{1}^{n-1}{r(4+(r-1)3) \over 2} \\=>2*n+\sum_{1}^{n-1}{r(1+3r) \over 2} \\=>2n+\sum_{1}^{n-1}{r \over 2}+\sum_{1}^{n-1}{3r^2 \over 2} \\=>2n+{(n-1)n \over 4}+{(2n-1)n(n-1) \over 4 }$