Q. If $S = 1.2 (2^{2} - 1^{2}) + 2.3 (3^{2} - 2^{2}) + 3.4 (4^{2} - 3^{2})$ + .... upto $50$ terms, then S is

2005 227 Sequences and Series Report Error

A

$50 (52)^{3}$

B

$50 \times (51)^{2} \times 26$

C

$49 (50)^{3}$

D

$50 \times (51)^{2} \times 13$

Solution:

$T_{r} = r (r + 1) [(r + 1)^{2} - r^{2}]$