https://file.aiquickdraw.com/mathbot/file/17264317056515xujhkyi.jpg

The expression provided in the image is:

\[
\frac{\sqrt{1}}{1^3} + \frac{\sqrt{2}}{2^3} + \frac{\sqrt{3}}{3^3}
\]

To write this sum in sigma notation, we observe that each term follows the pattern:

\[
\frac{\sqrt{n}}{n^3}
\]

where \(n\) starts at 1 and increases by 1 for each successive term. This can be written as:

\[
\sum_{n=1}^{3} \frac{\sqrt{n}}{n^3}
\]

Would you like more details on this or have any questions?

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Here are 5 related questions:
1. How would you expand the sigma notation if the sum continued for more terms?
2. Can you apply sigma notation for sums involving different powers of \(n\)?
3. How does changing the exponent on the denominator affect the sum?
4. What happens if the square root is replaced with another function, like a logarithm?
5. How do you convert a sigma notation into a general term for larger sums?

**Tip:** Sigma notation is a powerful tool to express series concisely, especially when dealing with sequences that follow a consistent pattern.

Write the sum using sigma notation for the series \( \frac{\sqrt{1}}{1^3} + \frac{\sqrt{2}}{2^3} + \frac{\sqrt{3}}{3^3} \).

Learn how to express the sum \( \frac{\sqrt{1}}{1^3} + \frac{\sqrt{2}}{2^3} + \frac{\sqrt{3}}{3^3} \) in sigma notation. Explore the use of summation symbols and pattern recognition in algebra, suitable for high school students.

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