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Question

Let fp(a)=eiap2e2iap2e3iap2eiap (Where i=1 and pN) then limnfn(π)

A
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B
i
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C
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D
i
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Solution

The correct option is C i
We have,
fp(a)=eiap2+2iap2+3iap2+........+piap2fp(a)=eiap2[1+2+3+.....p]fp(a)=eiap2p(p+1)2fp(π)=eiπ(x+1)2nlimnfn(π)=elimniπ(n+1)2n=eiπ2=cos(π2)+isin(π2)=iHence,optionBiscorrectanswer.

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