MathDB

Given the function

f(x) = x^2

, the sector of

f

from

a

b

is defined as the limited region between the graph of

y = f(x)

and the straight line segment that joins the points

(a, f(a))

and

(b, f(b))

. Define the increasing sequence

x_0

x_1, \cdots

with

x_0 = 0

and

x_1 = 1

, such that the area of the sector of

f

from

x_n

x_{n+1}

is constant for

n \geq 0

. Determine the value of

x_n

in function of

n

1