Sequences and Series: Series identity MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

Timer-based practiceDetailed answer reviewMobile-friendly flow

Series identityHardQuestion 210036

Question

The value of 1·2·3 + 2·3·4 + ... + n(n+1)(n+2) is:

A
n(n+1)(n+2)(n+3)/4
Correct
B
n(n+1)(n+2)/3
C
[n(n+1)/2]²
D
n²(n+1)²/4

Correct answer

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

Explanation

General term: r(r+1)(r+2). Summation of products of consecutive integers: Σ r(r+1)(r+2) = n(n+1)(n+2)(n+3)/4. This follows from the general formula Σ C(r+k, k+1).

Review Sequences and Series notes Start timed chapter practice