Therefore, the simplified function is:f(x) = (1-x)^4

[Phuzz]

1. Sum the Geometric Series 1-x+x²-x³+x⁴

and hence simplify the function

[f(x)]⁴ = 1 - x⁵
1-x+x²-x³+x⁴

Homework Equations

3. Not sure I quite get understand this properly, as my attempt doesn't seem quite right.


Basically I've gotten

S=1-x+x²-x³+x⁴

S=1-1+x-x²+x³
x x

which then subtracted becomes

s(1 - 1) = (1-1)+2x+x+x
x x

= 1 +4x
x

Then, putting that into the simplifying function part gives me

f(x) =

1 -x5
-1 +4x
x

 

[jeffreydk]

Notice that

$$1-x+x^2-x^3+\ldots=\sum_{n=0}^{\infty}(-1)^nx^n=\sum_{n=0}^{\infty}(-x)^n$$