Passage - 1 (Questions 60 to 62) Tangent at a point [other than ] on the curve meets…

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Passage - 1 (Questions 60 to 62) Tangent at a point

P_1

[other than

(0,0)

] on the curve

y=x^3

meets the curve again at

P_2

. The tangent at

P_2

meets the curve again at

P_3

and so on. If

P_1

has coordinates

(1,1)

, then the sum

\lim_{n\rightarrow\infty}\sum_{r=1}^n \frac{1}{x_n}

is (where

x_1,x_2,\dots

are abscissas of

P_1,P_2,\dots

, respectively) (a)

2/3

(b)

1/3

(c)

1/2

(d)

3/2