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1. Sum the Geometric Series 1-x+x^{2}-x^{3}+x^{4}
and hence simplify the function
[f(x)]^{4} = 1 - x^{5}
1-x+x^{2}-x^{3}+x^{4}
3. Not sure I quite get understand this properly, as my attempt doesnt seem quite right.
Basically Ive gotten
S=1-x+x^{2}-x^{3}+x^{4}
S=1-1+x-x^{2}+x^{3}
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
and hence simplify the function
[f(x)]^{4} = 1 - x^{5}
1-x+x^{2}-x^{3}+x^{4}
Homework Equations
3. Not sure I quite get understand this properly, as my attempt doesnt seem quite right.
Basically Ive gotten
S=1-x+x^{2}-x^{3}+x^{4}
S=1-1+x-x^{2}+x^{3}
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
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