Working with binomial series Use properties of power series, substitution, and factoring to find the first four nonzero terms of the Maclaurin series for the

Falak Kinney

Falak Kinney

Answered question

2021-03-07

Working with binomial series Use properties of power series, substitution, and factoring to find the first four nonzero terms of the Maclaurin series for the following functions. Use the Maclaurin series
(1+x)2=12x+3x24x3+ for 1
(1+4x)2

Answer & Explanation

opsadnojD

opsadnojD

Skilled2021-03-08Added 95 answers

Working with binomial series Use properties of power series, substitution, and factoring to find the first four nonzero terms of the Maclaurin series for the following functions. Use the Maclaurin series
(1+x)2=12x+3x24x3+, for 1
(1+4x)2
The Maclaurin series is (1+x)2=12x+3x24x3+...
Now obtain the series (1+4x)2 by substituting x=4x in the series of (1+x)2=12x+3x24x3+... and simplify.
Therefore,
(1+4x)2=12(4x)+3(4x)24(4x)3+...
=18x+3(16)x24(64)x3+...
=18x+3(16)x24(64)x3+...
Thus, the maclurin series (1+4x)2=18x+48x2256x3+

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-16Added 2605 answers

Answer is given below (on video)

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