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The question appears to be asking how to transition from the first step to the second in a mathematical expression involving the manipulation of sums and simplifications. Let's break down the relevant steps in the image.

### Given Expression:
The first line shows:
\[
\sqrt[n]{n - 1} - 1 = \frac{n - 1}{n + n + n + \cdots + 1}
\]

This is essentially taking the expression \(n - 1\), rewriting it in a form that can be manipulated in a sum over terms divided by \(n\).

### Transition to the Second Line:

In the second line, the transition involves rewriting the denominator, which was a sum of terms, into a simplified fractional form:
\[
\frac{n - 1}{n \cdot \sqrt{n}} 
\]

Here's the reasoning behind this:
1. **Denominator Simplification**: In the first line, the sum in the denominator is expressed as:
   \[
   n + (n-1) + (n-2) + \cdots + 1
   \]
   This is a simple arithmetic series. The sum of an arithmetic series with terms from 1 to \(n\) is:
   \[
   S = \frac{n(n+1)}{2}
   \]
   This approximation simplifies the denominator.

2. **Fraction Handling**: The numerator remains \(n-1\), while the denominator simplifies as an approximation:
   \[
   n \cdot \sqrt{n}
   \]
   This step assumes that \(n\) is large, allowing some of the finer terms to be neglected, leading to an approximation.

### Resulting Approximation:
The result of simplifying these terms gives:
\[
\frac{n - 1}{n \cdot \sqrt{n}} < \frac{n^{\frac{1}{2n}}}{\sqrt{n}} < \frac{2}{\sqrt{n}}
\]

This inequality comes from approximating the terms further and bounding the result.

Would you like more detailed information about any specific steps or need more examples on this kind of simplification?

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Here are five relative questions:
1. What are the steps to sum an arithmetic series and apply approximations for large \(n\)?
2. How can you justify ignoring small terms when approximating series or sums?
3. What are some typical applications of inequalities like the one shown here in mathematical proofs?
4. How can we apply similar techniques to simplify sums in calculus or combinatorics?
5. What happens when \(n\) approaches infinity in these kinds of limits?

**Tip**: Understanding how to simplify large sums and apply approximations for large \(n\) is useful in many areas of advanced mathematics, such as asymptotic analysis and algorithm complexity.

Learn how to transition from step 1 to step 2 in simplifying series involving the expression n^(1/2n) and applying approximations and inequalities for large n. This solution covers series simplifications, approximations, and the arithmetic series sum, aimed at advanced students.

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