For all positive integers n, the number n(n^2 − 1) is divisible b… - Vidyadip

MCQ

For all positive integers $n$, the number $n(n^2 − 1)$ is divisible by:

A
$36$
B
$24$
✓
$6$
D
$16$

✓

Answer

Correct option: C.

$6$

Given,
number $= n(n^2 - 1)$
Let $n = 1, 2, 3, 4….$
$n(n^2 - 1) = 1(1 - 1) = 0$
$n(n^2 - 1) = 2(4 - 1) = 2 \times 3 = 6$
$n(n^2 - 1) = 3(9 - 1) = 3 \times 8 = 24$
$n(n^2 - 1) = 4(16 - 1) = 4 \times 15 = 60$
Since all these numbers are divisible by $6$ for $n = 1, 2, 3,..........$
So, the given number is divisible $6$

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