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Question: If I<sub>n</sub> = <img src="https://cdn.pureessence.tech/canvas_88.png?top_left_x=951&top_left_y=60...

If In = (n Î N), then n(In–1 + In+1), is equal to -

A

p/2

B

p

C

1

D

2

Answer

1

Explanation

Solution

In–1 + In+1 = ∫0π/4(tan⁡n−1θ+tan⁡n+1θ)dθ\int _ { 0 } ^ { \pi / 4 } \left( \tan ^ { \mathrm { n } - 1 } \theta + \tan ^ { \mathrm { n } + 1 } \theta \right) \mathrm { d } \theta

= =

= 1n\frac { 1 } { \mathrm { n } }

̃ n(In–1 + In+1) = 1