   Chapter 11.10, Problem 52E

Chapter
Section
Textbook Problem

# (a) Expand 1 / 1 + x 4 as a power series.(b) Use part (a) to estimate 1 / 1.1 4 correct to three decimal places.

(a)

To determine

To expand: The function 11+x4 .

Explanation

Given:

The function is 11+x4 .

Result used:

The Binomial series: If k is any number and |x|<1 then, (1+x)k can be expressed as

(1+x)k=n=1(kn)xn=1+kx+k(k1)2!x2+k(k1)(k2)3!+ (1)

Calculation:

The given function is expressed as,

11+x4=(1+x)14

Substitute 14 for k in equation (1),

11+x4=n=1(14n)xn=[1+(14)x+(14)(141)2!x2+(14)(141)(142)3!x3                                           +14(141)(14(n1))n!xn+]                                =[114x+(14)(144)2!x2+(14)(

(b)

To determine

To estimate: The sum 11.14 correct to three decimal places.

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