First slide

Binomial theorem for positive integral Index

Question

For all $n \in N, n (n + 1) (2 n + 1)$ is divisible by

Moderate

A

6
B

8
C

15
D

9

Solution

We have $n (n + 1) (2 n + 1) = 6 \{1^{2} + 2^{2} + \dots + n^{2}\}$ ,
$∴ n (n + 1) (2 n + 1)$ is divisible by 6 for all $n \in N$ .

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