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Question

Find the values of (1)n+(1)2n+(1)2n+1+(1)4n+1, where n is any positive odd integer.

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Solution

Let x=(1)n+(1)2n+(1)2n+1+(1)4n+1
where n is odd.
(1)n=1(1)2n=1(1)2n+1=(1)2n.(1)=1(1)4n+1=(1)4n(1)=1x=1+111=2

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