If a_n= _0^ /2 ^2nx x ,dx then a_2-a_1, a_3-a_2, a_4-a_3, are in

JEE Advanced Mathematics question

If then are in

Answer: (C)

First simplify the numerator of :

nx-(n-1)x= .

Apply :

=(2n-1)x· x .

(Equivalently, use .) The cancels, so

-=^{π/

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Question ID VK-109494