For any positive integer n, let S_n : (0, ) R be defined by S_n(x) = _ k=1 ^ n ^ -1 ( 1 + k(k+1)x^2 x ), where for any x R , ^ -1 (x) (0, ) and ^ -1 (x) (- 2 , 2 ). Then which of the following statements is (are) TRUE ?

JEE Advanced 2021 Mathematics question

For any positive integer , let be defined by

= (),

where for any , and . Then which of the following statements is (are) TRUE ?

Answer: (A),(B)

For the argument is positive, so . Telescoping: . (A) $ =

Create a free account to read the complete working, and practise questions like this in a timed test.

Question ID VK-033892