Rút gọn A

To simplify the series presented for \( A \), \( B \), and \( C \), we can break down each term.

1. **For \( A \)**:
The series can be expressed as:
\[
A = \frac{1}{1.2^3} + \frac{1}{2.3.4} + \frac{1}{3.4.5} + \ldots + \frac{1}{99.100.101}
\]
This can be recognized as a summation of fractions with specific polynomial denominators.

2. **For \( B \)**:
The series is:
\[
B = \frac{1}{3.5} + \frac{1}{4.5.7} + \frac{1}{5.7.9} + \ldots + \text{(up to 2021, 2023, 2025)}
\]
Similar to \( A \), this series will need to be transformed based on the patterns in denominators.

3. **For \( C \)**:
The series
\[
C = \frac{1}{1^1} + \frac{1}{2^2} + \frac{1}{3^3} + \ldots + \frac{1}{100^100}
\]
can be calculated based on the general term \( \frac{1}{n^n} \).

### General Approach for Rút gọn:

- **Pattern Recognition**: Identify patterns in the series to find a general formula.
- **Summation Techniques**: Use known formulas for summations or convergent series.
- **Approximation / Convergence**: If the terms decrease significantly, you may approximate or find convergence.

If you need specific numerical approximations or detailed symbolic expressions, please specify which part you are most interested in!