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Let $I_{n} = \int_{0}^{π / 4} \tan^{n} x d x .$ Then $I_{2} + I_{4}, I_{3} + I_{5}, I_{4} + I_{6}, I_{5} + I_{7}, \dots$ are in

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Correct option is C

We have for r≥2,Ir+Ir+2=∫0π/4 tanr⁡x1+tan2⁡xdx =∫0π/4 tanr⁡xsec2⁡xdx =1r+1tanr+1⁡x0π/4=1r+1Thus, the given sequence becomes, 13,14,15,16,…This is clearly an H.P.

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Let In=∫0π/4 tann⁡xdx. Then I2+I4,I3+I5,I4+I6,I5+I7,…are in

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Let $I_{n} = \int_{0}^{π / 4} \tan^{n} x d x .$ Then $I_{2} + I_{4}, I_{3} + I_{5}, I_{4} + I_{6}, I_{5} + I_{7}, \dots$ are in