https://file.aiquickdraw.com/mathbot/file/1729365358335hver55tk.jpg

The expression in the image can be interpreted as:

\[
1 + \left( \frac{1}{2} + \frac{1}{2} \right) + \left( \frac{1}{3} + \frac{1}{3} + \frac{1}{3} \right) + \cdots + \left( \frac{1}{100} + \frac{1}{100} + \cdots + \frac{1}{100} \right)
\]

Each group inside parentheses seems to follow a pattern where the fraction \(\frac{1}{n}\) is repeated \(n\) times. So, for the term \(\frac{1}{n}\) repeated \(n\) times, it can be simplified as:

\[
\frac{1}{n} + \frac{1}{n} + \cdots + \frac{1}{n} \text{ (n terms)} = \frac{n}{n} = 1
\]

Therefore, each group of terms inside the parentheses simplifies to 1. If we write it out, we have:

\[
1 + 1 + 1 + \cdots + 1 \text{ (100 terms)}
\]

This sum consists of 100 terms, each equal to 1, so the total sum is:

\[
100
\]

Thus, the value of the given expression is:

\[
\boxed{100}
\]

Would you like further explanation on any step, or do you have additional questions?

Here are 5 related questions to consider:
1. How can we identify patterns in series and sequences?
2. What is the significance of simplifying sums of fractions?
3. How do harmonic series differ from this pattern?
4. What are common techniques for summing arithmetic sequences?
5. How can we use summation notation to represent complex sums?

**Tip**: Simplifying repeated terms is a common strategy in series. Identifying patterns early helps to avoid unnecessary calculations.

1 + (1/2 + 1/2) + (1/3 + 1/3 + 1/3) + ... + (1/100 + 1/100 + ... + 1/100) = ?

Learn how to sum repeated fractional terms like (1/n repeated n times) in a series up to 100. This arithmetic sequence simplifies each set to 1, resulting in a total sum of 100. Ideal for students in Grades 9-10.

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