Question

find the sum of 1*2+2*3+3*4upto n terms​

Answer 1

Answer:

$\frac{n(n+1)^2}{3}$

Step-by-step explanation:

sum=∑

$1*2+2*3+3*4+..........+n(n+1)\\It \;\;can\;\;be\;replaced\;\;by\\sum\;\;of\;\;n^2+n\;\;i.e.n(n+1)\\\\=sum(n^2)+sum(n)\\\\=\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}\\\\=\frac{n(n+1)}{2}(\frac{2n+1}{3}+1)\\\\=\frac{n(n+1)}{2}(\frac{2n+4}{3})\\\\=\frac{n(n+1)^2}{3}$

Hope it Helps