What is the sum of first 20 terms of the following series?
1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + . . . . . . . .

Solution (By Examveda Team)

$$\eqalign{ & {\text{Sum,}} \cr & {S_n} = \frac{{n\left( {n + 1} \right)\left( {n + 2} \right)}}{3} \cr & {S_{20}} = \frac{{20 \times 21 \times 22}}{3} \cr & = 140 \times 22 \cr & = 3080 \cr} $$