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Ionic Radii and Ionisation Enthalpy (Group 2)

The largest n...

Question

The largest number that exactly divides each number in the sequence $(1^{5} - 1), (2^{5} - 2), (3^{5} - 3), (4^{5} - 4), . . . . (n^{5} - n)$ is:

A

1

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B

15

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C

30

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D

120

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Solution

The correct option is C 30
The series can be expanded as- $0, 30, 240, . . .$
The lowest non-zero number is 30, hence it can be easily verified that all the numbers are divisible by 30.

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