Math Problem Statement

\( \lim_{n \to \infty} \sum_{k=1}^{n} \frac{k}{(n+1)^k} \)

Solution

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Please give me a moment to examine it further.From what I can see in the image, the problem involves calculating a summation or a limit with factorials. The exact details aren't entirely clear, but it looks like you're dealing with an expression of the form:

lim⁡n→∞∑k=1nk(n+1)k\lim_{n \to \infty} \sum_{k=1}^{n} \frac{k}{(n+1)^k}

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Math Problem Analysis

Mathematical Concepts

Calculus
Series and Summation
Limits
Factorials

Formulas

Summation Formula: \( \sum_{k=1}^{n} a_k \)
Limit Definition: \( \lim_{n \to \infty} a_n \)
Geometric Series Sum Formula: \( \sum_{k=0}^{\infty} ar^k = \frac{a}{1-r} \) for |r| < 1

Theorems

Limit Theorem
Convergence of Series

Suitable Grade Level

College Level

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