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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]
f(x) = 7(1 − x)−2
f(x) =
[infinity] sum.gif
n = 0
Find the associated radius of convergence R.
R =

Respuesta :

varshamittal029

The radius of convergence R of the given function f(x) = (-1)^n(1 - x)² be,

R = 1/2.

Given, a function f(x)

f(x) = (-1)^n(1 - x)²

we have to find the radius of convergence R of the given function,

first will find the (n+1)th term of the given function

as, an = (-1)^n(1 - x)²

then an+1 = (-1)^(n+1)(1 - x)²

to find the radius of convergence, we will find

lim x->∞ an+1/an

lim x->∞ ((-1)^(n+1)(1 - x)²)/((-1)^n(1 - x)²)

On solving the limits, we get

lim x->∞ an+1/an = 2x

then R = 1/2

as, -1/2 < x < 1/2

so, the radius of the convergence be, 1/2

Hence, the radius of the convergence be, 1/2

Learn more about Radius of Convergence here https://brainly.com/question/28209832

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