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Find Power Series and interval of convergence

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1 Answer

Start with
ex = 1 + x + x²/2! + x³/3! + ... = ∑n=0 xn/n!, which converges everywhere.
Therefore,
 
x e5x = x ∑n=0 (5x)n/n! = ∑n=0 5n xn+1/n!, which also converges everywhere.