Using known series and algabraic operations obtain the first

Using known series and algabraic operations, obtain the first four non zero terms in the power series (in powers of x), for the function (e^-x)cosx.

Solution

exoand both series :
e-x = 1 - x + x*x/2! - x*x*x/3! ....

cosx = 1 - x*x/2! + x*x*x*x/4! ...

e-x cosx = 1 -x + 2x*x*x/3! + 2x*x*x*x/4! .....   first four terms !!!

Using known series and algabraic operations, obtain the first four non zero terms in the power series (in powers of x), for the function (e^-x)cosx. Solutionexo

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