https://file.aiquickdraw.com/mathbot/file/1726199139529vga8j5d2.jpg

The image shows part of a mathematical sequence where the first two terms, \( a_1 \) and \( a_2 \), are being defined.

From what I can see:
- \( a_1 = \frac{1}{1(1+1)} \)
- \( a_2 = \frac{1}{2(2+1)} \)

It looks like you are working with a sequence where each term is of the form:

\[
a_n = \frac{1}{n(n+1)}
\]

Would you like me to explain this sequence further, solve for more terms, or explain its properties in detail?

### Related Questions:
1. What is the general formula for the \( n \)-th term of this sequence?
2. How does this sequence behave as \( n \) approaches infinity?
3. Can this sequence be summed, and what is the sum of the series?
4. What is the partial sum \( S_n = a_1 + a_2 + \dots + a_n \) of this sequence?
5. How does this sequence relate to the harmonic series or other known series?

### Tip:
This sequence can be simplified further using partial fraction decomposition for sums, which is a useful tool in calculus.

The user submitted a sequence problem where the first two terms of the sequence are shown:
a1 = 1 / (1(1+1))
a2 = 1 / (2(2+1))

This webpage explains the mathematical sequence where each term is defined by a_n = 1 / (n(n+1)). Learn how to find the general term, analyze its behavior, and explore related series concepts. Suitable for students in Grades 9-12.

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