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

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite 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 co-ordinates

(1,1)

, then the sum

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

is (where

y_1,y_2,\dots

are ordinates of

P_1,P_2,\dots

, respectively.) (a)

1/8

(b)

1/9

(c)

8/9

(d)

9/8