Series Power
Series Power
How do I represent this function as a power series?
Represent f(x) = 2/(x+5) as a power series using the geometric series about x=1.
Geometric series:
f(x)=1/(1-x)=∑[n=0 to ∞] xⁿ = 1+x+x²+x³+x⁴+ ...
f(x) = 2/(x+5) = (2/5)/(1+x/5) = (2/5)/[1 -(-x/5)] =
(2/5)*∑[n=0 to ∞] (-x/5)ⁿ = ∑[n=0 to ∞] [2*(-1)ⁿ/5ⁿ⁺¹]*xⁿ =
(2/5) -2x/25+2x²/125 -2x³/625+ ...
Radius of convergence:
|-x/5|<1 ==> |x|<5
R=5
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