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Q.

If f is a positive function such that f(x+T)=f(x) ,(T>0),xR then limnn(f(x+T)+2f(x+2T)+..+nf(x+nT)f(x+T)+4f(x+4T)+..+n2f(x+n2T))=

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a

2

b

23

c

3

d

32

answer is C.

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Detailed Solution

f(x+T)=f(x+2T)=..=f(x+nT)=f(x) limnnf(x)(1+2+3+.+n)f(x)(1+22+32++n2)=limnn(n(n+1)2)n(n+1)(2n+1)6=32

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