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Algebra Level 2

What is the sum of the following series- ( 1.2.3 + 2.3.4 + 3.4.5........... 1.2.3+2.3.4+3.4.5........... ) upto n terms?

(n(n+1)(n+2)(n+3))/3 (n(n+1)(n+2)(n+3))/4 (n(n+2)(n-3)(n+4))/4 (n(n+1)(n+2)(n-3))/3

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1 solution

Varun Shekhar
Apr 13, 2018

we see that the nth term of the sequence is n(n+1)(n+2). n(n+1)(n+2)= n 3 + 3 n 2 + 2 n n^3+3n^2+2n now after applying summation we get the answer as- n ( n + 1 ) ( n + 2 ) ( n + 3 ) 4 \frac{n(n+1)(n+2)(n+3)}{4}

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