Consider the curve and a point on it

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Consider the curve

y = \tan^{-1} x

and a point

A\left(1, \frac{\pi}{4}\right)

on it. If the variable point

P_i(x_i, y_i)

moves on the curve for

i = 1, 2, 3, \dots, n

(

n \in \mathbb{N}

) such that

y_r = \sum_{m=1}^{r} \tan^{-1}\left(\frac{1}{2m^2}\right)

and

B(x, y)

be the limiting position of variable point

P_n

n \to \infty

, then the value of reciprocal of the slope of

AB

will be