answer: - x¹¹\n#____ - find the sum of 1 + 5/...

answer: - x¹¹\n#____ - find the sum of 1 + 5/1! + 25/2! + 125/3! + ⋯ + 5ⁿ/n! + ⋯

Answer

# Explanation: ## Step1: Recall the exponential - series formula The Maclaurin series for the exponential function is $e^{x}=\sum_{n = 0}^{\infty}\frac{x^{n}}{n!}=1+\frac{x}{1!}+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+\cdots+\frac{x^{n}}{n!}+\cdots$. ## Step2: Identify the value of x In the given series $1+\frac{5}{1!}+\frac{25}{2!}+\frac{125}{3!}+\cdots+\frac{5^{n}}{n!}+\cdots$, we can see that $x = 5$. # Answer: $e^{5}$