Use the power series 1/1+x = Σ∞ n=0 (-1)ⁿ xⁿ , Ixl

Question

Use the power series
1/1+x = Σ∞ n=0 (-1)ⁿ xⁿ , Ixl < 1
to determine a power series for the function, centered at 0,
f(x) = 18/(x+1)³ = d²/dx² (9/x+1]
f(x) = Σ∞ n=0 (-1)ⁿ xⁿ . (n+2)!/n!
Determine the interval of convergence. (Enter your answer using interval notation.)
(-1,1)

Kunduz · Accepted Answer

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Use the power series 1/1+x = Σ∞ n=0 (-1)ⁿ xⁿ , Ixl < 1 to