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Power series/R/Fourth power/Fifth coefficient/Exercise
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Let
∑
n
=
0
∞
a
n
x
n
{\displaystyle \sum _{n=0}^{\infty }a_{n}x^{n}}
be an absolutely convergent power series. Determine the coefficients of the powers
x
0
,
x
1
,
x
2
,
x
3
,
x
4
,
x
5
{\displaystyle {}x^{0},x^{1},x^{2},x^{3},x^{4},x^{5}}
in the fourth power
∑
n
=
0
∞
c
n
x
n
=
(
∑
n
=
0
∞
a
n
x
n
)
4
.
{\displaystyle {}\sum _{n=0}^{\infty }c_{n}x^{n}={\left(\sum _{n=0}^{\infty }a_{n}x^{n}\right)}^{4}\,.}
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