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Question

If n is a positive integer, then (3+1)2n(31)2n is :

A
an irrational number
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B
an odd positive interger
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C
an even positive interger
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D
a rational number other than positive integers
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Solution

The correct option is A an irrational number
(3+1)2n(31)2n=[(3+1)2]n[(31)2]n=(4+23)n(423)n=2n[(2+3)n(23)n]=2n×2[nC12n13+nC3.2n333+...]=2n+13[nC12n1+nC32n33+....]
=3×Some integer irrational number

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