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## Homework Statement

(a) Expand f(x) as a power series

[tex]f(x)=\frac{7}_{\sqrt[4]{1+\frac{x}_{14}}}[/tex]

Which I converted to....

[tex]7 - \frac{1}{8}*x + \sum^{\infty}_{n=2}7*(-1)^{n}*\frac{1*5*9*...*(4n-3)}{4^{n}*n!}*(\frac{x}{14})^{n}[/tex]

(b) Use part (a) to estimate 7 / (1.1)^(1/4) correct to three decimal places.

## Homework Equations

Knowledge of Taylor & Maclaurin Series

## The Attempt at a Solution

[tex]7 - \frac{1}{8}*(1.1) + \sum^{\infty}_{n=2}7*(-1)^{n}*\frac{1*5*9*...*(4n-3)}{4^{n}*n!}*(\frac{1.1}{14})^{n}[/tex]

=0.981268

Though, I think this is more on the right track:

1.1=1+x/14

.1=x/14

1.4=x

[tex]7 - \frac{1}{8}*(1.4) + \sum^{\infty}_{n=2}7*(-1)^{n}*\frac{1*5*9*...*(4n-3)}{4^{n}*n!}*(\frac{1.4}{14})^{n}[/tex]

=0.976454

As always, any guidance will be appreciated and thanked =)

Sincerely,

NastyAccident