https://file.aiquickdraw.com/mathbot/file/1724876483884u8go5z1q.jpg

The image contains a mathematical expression that appears to be a recurrence relation or a sum, along with a question in Spanish asking if the result is true or false.

The expression given seems to define a series \( P(n) \) as:

\[
P(n) = 1^3 + 2^3 + 3^3 + \dots + n^3 = \left(\frac{n(n+1)}{2}\right)^2
\]

The question asks if the provided equation is true, which implies whether the sum of cubes of the first \( n \) natural numbers equals the square of the sum of the first \( n \) natural numbers.

### Analysis:
- The sum of cubes of the first \( n \) natural numbers is indeed given by:
  \[
  1^3 + 2^3 + 3^3 + \dots + n^3 = \left(\frac{n(n+1)}{2}\right)^2
  \]
- The right-hand side of the equation represents the square of the sum of the first \( n \) natural numbers. 

This is a well-known identity in mathematics, and it is correct.

### Conclusion:
The statement in the image is **True**.

Would you like any more details, or do you have any questions? 

Here are five related questions to consider:
1. How is the formula for the sum of cubes derived?
2. Can the sum of squares of the first \( n \) numbers be related to the sum of cubes?
3. What other identities involving sums of powers are there?
4. How would the formula change for different powers, such as the fourth or fifth power?
5. How can this formula be used in practical applications?

**Tip:** When dealing with sums of powers, familiarizing yourself with standard formulas and identities can save a lot of time.

Explore the sum of cubes formula in mathematics: 1^3 + 2^3 + ... + n^3 = (n(n+1)/2)^2. This formula explains how the sum of cubes of the first n natural numbers equals the square of the sum of these numbers. Learn its derivation, applications, and related mathematical identities.

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