- #1
NastyAccident
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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 =)
NastyAccident