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?

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.