Answers

2014-02-22T18:54:18+05:30
1.2.3+2.3.4+.....+n(n+1)(n+2) = ∑n(n+1)(n+2)
=∑n(n²+3n+2)
Applying ∑ to every number
=∑n³+ ∑3n²+∑2n
=n²(n+1)²/4 + 3{n(n+1)(2n+1)/6 +2n(n+1)/2
=n(n+1)/2{n(n+1)/2+ (2n+1)+2}
=n(n+1)/2{(n²+n)+ (4n+2)+4}/2
=n(n+1){(n²+5n+6}/4
=n(n+1)(n+2)(n+3)/4
2 5 2