Question

Question

✔1× 2×3+ 2×3×4+------------ n(n-1)(n+2)= n(n+1)(n+2)(n+3)/4

✔1×2+2×3+3×4+-------- +n(n+1)[n(n+1)(n+2)/3]

Answer 1

See the attachments I hope it will help you^_^

Thanks ❤:)

#Nishu HarYanvi ♥

Answer 2

Heyy mate ❤✌✌❤

Here's your Answer.

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1.

What is the sum to ‘n’ terms of the series: 1.2.3 + 2.3.4 + 3.4.5 +…?

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10 ANSWERS

Naveen Shekhar, works at Assistant Administrative Officer ,LIC of India (2012-present)

Answered Oct 1, 2017 · Author has 233answers and 300.5k answer views

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.

2.

LHS = (1) (2) = 2

RHS = 1 × 2 × 3/3

=> R.H.S = 2.

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