Question:

Consider the series \[\sum_{n=1}^{\infty} n^m \left(\frac{1}{1 + \frac{1}{n^p}}\right)\] where \( m \) and \( p \) are real numbers. Under which of the following conditions does the above series converge?

Updated On: Oct 1, 2024
  • \( m > 1 \).
  • \( 0 < m < 1 \) and \( p > 1 \).
  • \( 0 < m \leq 1 \) and \( 0 \leq p \leq 1 \).
  • \( m = 1 \) and \( p > 1 \).
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The Correct Option is A

Solution and Explanation

The correct option is (A): \( m > 1 \).
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