a) Find the Maclaurin series for the function f(x)=frac11+x b) Use differentiation of power series and the result of part a) to find the Maclaurin ser

Khadija Wells

Khadija Wells

Answered question

2020-10-19

a) Find the Maclaurin series for the function
f(x)=11+x
b) Use differentiation of power series and the result of part a) to find the Maclaurin series for the function
g(x)=1(x+1)2
c) Use differentiation of power series and the result of part b) to find the Maclaurin series for the function
h(x)=1(x+1)3
d) Find the sum of the series
n=3n(n1)2n
This is a Taylor series problem, I understand parts a - c but I do not understand how to do part d where the answer is 72

Answer & Explanation

Nathalie Redfern

Nathalie Redfern

Skilled2020-10-20Added 99 answers

It took me a while to get this, but finally I got it. Had to try a lot of tricks to get this series.
We have the series for 1(x+1)3 as shown below:
f(x)=1(1+x)3=n=012(1)n(n+1)(n+2)xn
We can similarly write a series for 1(1x)3 as shown below:
f(x)=1(1x)3=n=012(n+1)(n+2)xn
Now, since the index of the summation in our question starts from n=3, we could shift the index of this series to n=3. I tried that, but it didnt
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-16Added 2605 answers

Answer is given below (on video)

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