The sum of the series 1+2 × 3+4+5 × 6+7+8 × 9+ ... up to 50 terms is

Question

The sum of the series 1+2 × 3+4+5 × 6+7+8 × 9+ ... up to 50 terms is (A) 48775 (B) 47825 (C) 49675 (D) 50000

Tardigrade Admin · Accepted Answer

S50= displaystyle ∑r=125[(3 r-2)+(3 r-1)(3 r)] = displaystyle ∑r=125(9 r2-2) =(9/6)(25)(26)(51)-50=49675

Q. The sum of the series $1 + 2 \times 3 + 4 + 5 \times 6 + 7 + 8 \times 9 +$ ... up to $50$ terms is