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Question

If In=π/40tannxdx, then I2+I4,I3+I5,I4+I6,I5+I7,....... are in

A
A.P
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B
G.P
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C
H.P
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D
none of these
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Solution

The correct option is D H.P
In+In+2=(tannx+tann+2x)dx
In+In+2=tannx.(1+tan2x)dx
In+In+2=tannx.sec2x.dx
By applying the limits of integration, In+In+2=tann+1π4n+1=1n+1
Terms of the form n+1 form an AP for successive n values.
Hence, their reciprocals 1n+1form an HP, for successive n values.

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