Question

2.3n+1+7.3n-1/3n+2-2(1/3)1-n

Answer 1

Answer:

Step-by-step explanation:nth term =n(n+1)(n+2); where n=1,2,3,…

=n(n^2+3n+2)=n^3 +3n^2 +2n

Now,note

Sum =n(n+1)/2 ; if nth term =n

=n(n+1)(2n+1)/6 ; if nth term =n^2

=n^2(n+1)^2/4 ; if nth term =n^3

Hence the required sum =

n^2(n+1)^2 /4 + 3 ×n(n+1)(2n+1)/6 +2 × n(n+1)/2

=n^2 (n+1)^2 /4 +n(n+1)(2n+1)/2 + n(n+1)

=n(n+1) { n(n+1)/4 + (2n+1)/2 +1 }

=n(n+1) { (n^2 +n +4n+2 +4)/4 }

=1/4 n(n+1){ n^2+5n+6 }

=1/4 n(n+1)(n+2)(n+3) Ans.