Mathematics, 31.01.2020 19:45 Perdikaris
(a) use differentiation to find a power series representation forf(x) =1(6 + x)2.f(x) =∞ leftparen1.gif(−1)n(n+1)xn6n+2 rightparen1.gifsum. gifn = 0what is the radius of convergence, r? r = (b) use part (a) to find a power series forf(x) =1(6 + x)3.f(x) =∞ leftparen1.gif(−1)n(n+3)(n+1)xn6n+5 rightparen1.gifsum. gifn = 0what is the radius of convergence, r? r = (c) use part (b) to find a power series forf(x) =x2(6 + x)3.f(x) =∞ leftparen1.gif(−1)n(n+2)(n+1)xn+26n +3 rightparen1.gifsum. gifn = 2what is the radius of convergence, r? r =
Answers: 1
, so that the radius of convergence is 
.
and we get
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(a) use differentiation to find a power series representation forf(x) =1(6 + x)2.f(x) =∞ leftparen1....
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