Use the binomial series to find the Maclaurin series for the function. f(x)=1(1+x)4

Rivka Thorpe

Rivka Thorpe

Answered

2020-11-20

Use the binomial series to find the Maclaurin series for the function.
f(x)=1(1+x)4

Answer & Explanation

pierretteA

pierretteA

Expert

2020-11-21Added 102 answers

We have to find Maclaurin series of the Function f(x)=1(1+x)4=(1+x)4 by using binomial series.
We know the binomial series
(1+x)α=n=0(αn)xn
Where (αn)=α(α1)(α2)...(αn+1)n!
We have given function
f(x)=1(1+x)4=(1+x)4
By binomial series
(1+x)4=n=0(4n)xn
=n=0(4)(41)(42)...(4n+1)n!xn
=n=0(4)(41)(42)...(4(n1))n!xn
=n=0(1)n4.5.6.7...(4+(n1))n!xn
Therefore f(x)=n=0(1)n4.5.6.7...(4+(n1))n!xn
Jeffrey Jordon

Jeffrey Jordon

Expert

2021-12-27Added 2575 answers

Answer is given below (on video)

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