Class 11

Math

Algebra

Sequences and Series

$1×2+2×3+3×4+....nterms=$

- $3n(n+1)(n+2) $
- $3n(n+1)(n−2) $
- $6n(n+1)(n+2) $
- $6n(n−1)(n−2) $

Then sum of $n$ terms $=r=1∑n n(n+1)=r=1∑n (n_{2}+n)$

$=r=1∑n n_{2}+r=1∑n n=6n(n+1)(2n+1) +2n(n+1) $

$=6n(n+1)(2n+1)+3n(n+1) $

$=6n(n+1)[2n+1+3] $

$=6n(n+1)(2n+4) $

$=3n(n+1)(n+2) $.