wayground logo

Free Printable Worksheets

NEW

Font size

S
M
L
XL
Worksheets

Chapter 11 - Power Series - and its representation as a function

Total questions: 3

Worksheet time: 10mins

Name
Class
Date
1.

Determine the radius of convergence of the power series ∑n=1∞x2n n!\sum_{n=1}^{\infty}\frac{x^{2n}\ }{n!}

a)

R=0R=0

b)

R=1R=1

c)

R=∞R=\infty

d)

R=12R=\frac{1}{2}

2.

The interval of convergence for ∑n=1 ∞  (5x−4)nn3\sum_{n=1\ }^{\infty\ }\frac{\ \left(5x-4\right)^n}{n^3} is equal to ____

a)

(25,65)\left(\frac{2}{5},\frac{6}{5}\right)

b)

[25,65]\left[\frac{2}{5},\frac{6}{5}\right]

c)

(35,1)\left(\frac{3}{5},1\right)

d)

[35,1]\left[\frac{3}{5},1\right]

3.

Consider the function f(x)=42x+3f\left(x\right)=\frac{4}{2x+3} . Find a proper power series representation for the function and determine the interval of convergence. Interval of convergence is _____

a)

(−32,32)\left(-\frac{3}{2},\frac{3}{2}\right)

b)

(−23,23)\left(-\frac{2}{3},\frac{2}{3}\right)

c)

(−2,2)\left(-2,2\right)

d)

(−43,43)\left(-\frac{4}{3},\frac{4}{3}\right)