Expressing a function as a power series

[jomelmaroma]

Hey guys! Suppose you have a function f(x)=1/2-x which you need to express as a power series. I am familiar with the conventional way of solving its series form, which involves taking out 1/2 from f(x) and arriving with a rational function 1/1-(x/2) which is easy to express as a power series.

I just had an idea: Since I can express f(x) as f(x)=1/(1+(1-x)), does that mean I can take r as 1-x such that the power series is summation from n=0 to infinity (1-x)^n?

Thanks!

 

[mathman]

Hey guys! Suppose you have a function f(x)=1/2-x which you need to express as a power series. I am familiar with the conventional way of solving its series form, which involves taking out 1/2 from f(x) and arriving with a rational function 1/1-(x/2) which is easy to express as a power series.

I just had an idea: Since I can express f(x) as f(x)=1/(1+(1-x)), does that mean I can take r as 1-x such that the power series is summation from n=0 to infinity (1-x)^n?

Thanks!

Series involving powers of x are called MacLaurin series. Series involving powers of (x-a), where a is constant are called Taylor series. What you are proposing is a Taylor series with a = 1.