SOLUTION: Hi All, Please can someone help Derive the Maclaurin series for sin x as sin x = x -x^3/3!+x^5/5! - ... Hence write down the Maclaurin series for x sin x and sin 3x. Th

Question 380324: Hi All, Please can someone help

Derive the Maclaurin series for sin x as
sin x = x -x^3/3!+x^5/5! - ...
Hence write down the Maclaurin series for x sin x and sin 3x.
Thank You
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Note the definition of a power series
(sorry, I can't put the f "prime" in without an error message being displayed)
If f(x) = sin x then its derivatives are:

etc.
The Maclaurin series is pretty much the same as a Taylor series except that it is centered around 0. Using the power series definition, we have

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