**Determine if the Following Series Converges or Diverges**In this exercise, you are to determine whether the series converges or diverges. Show your work carefully.\[ \sum_{n=1}^{\infty} \frac{1}{\sqrt{n+1} + \sqrt{n}} \]**Explanation:**We need to analyze the given series to see if it reaches a finite limit or not. This is done by either performing a mathematical convergence test or transforming the series into a recognizable form that we know converges or diverges.**Hints for Solution:**- Consider the manipulation of the terms inside the series.- Apply tests for convergence, such as the Ratio Test, Root Test, or Comparison Test.- Simplify the expression to check for any properties or limits that can help reach a conclusion.This problem encourages understanding the basics of infinite series and their behavior, a critical concept in higher-level mathematics.**Note:**Please solve step by step and be careful with algebraic manipulations.

Name: **Determine if the Following Series Converges or Diverges**In this ex
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: **Determine if the Following Series Converges or Diverges**In this exercise, you are to determine whether the series converges or diverges. Show your work carefully.\[ \sum_{n=1}^{\infty} \frac{1}{\sqrt{n+1} + \sqrt{n}} \]**Explanation:**We need to