JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Application +4 | -1

The sum of the series

1 \cdot 2 \cdot 3 + 2 \cdot 3 \cdot 4 + 3 \cdot 4 \cdot 5 + ...

n

terms is

View answer and explanation

Correct option: C

\frac{1}{4}n\left( {n + 1} \right)\left( {n + 2} \right)\left( {n + 3} \right)

Option C (

\frac{1}{4}n(n + 1)(n + 2)(n + 3)

) is correct because it represents the sum of the series

1 \cdot 2 \cdot 3 + 2 \cdot 3 \cdot 4 + 3 \cdot 4 \cdot 5 + ...

n

terms, which can be found by expressing the general term as

n(n+1)(n+2)

and summing it.

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