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Question

If Sn is the sum of the first n even natural numbers, then which of the following leave no remainder on dividing Sn ?


A

n

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B

n+1

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C

n and (n+1) both

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D

n-1

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Solution

The correct option is C

n and (n+1) both


Since the sequence is a series of ‘n’ even numbers, the sequence is 2,4,6,8,…

The common difference, d =t2t1 = 4 – 2 = 2.

The first term, a = 2

Sum to ‘n’ terms,

Sn = n2(2a+(n1)d)

Sn = n2(2×2+(n1)2)

Sn = n2(4+2n2)

Sn = n2(2n+2)

Sn = n(n+1)

i.e, Sn is divisible by n and n+1.


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