X∞k=0limn→∞n(n − 1)(n − 2)· · ·(n − k + 1)nkxk

To answer the given question, we need to understand the expression provided. The expression appears to be a mathematical series involving a limit and a product notation.

Let's break down the expression step by step:

1. The expression starts with "X∞k=0," which indicates a summation notation. The symbol "X" represents the summation, "k" is the index variable, and "0" and "∞" represent the lower and upper limits of the summation, respectively.

2. Next, we have "limn→∞," which denotes a limit as "n" approaches infinity. This means we are interested in the behavior of the expression as "n" becomes larger and larger.

3. Inside the summation, we have a product notation "(n − 1)(n − 2)· · ·(n − k + 1)." This indicates that we are multiplying a series of terms together. The terms are obtained by subtracting "k" from "n" and adding 1.

4. After the product notation, we have "nkxk." This term suggests that each term in the product is multiplied by "nkxk," where "x" is a constant.

To fully understand the expression and provide a more specific answer, we would need additional information or context.