What is the value of the sum $\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \cdots + \frac{1}{n(n+1)} +\cdots + \frac{1}{9900}$? Express your answer as a common fraction.
Question:
What is the value of the sum $\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \cdots + \frac{1}{n(n+1)} +\cdots + \frac{1}{9900}$? Express your answer as a common fraction.
Answer:
Let's think step by step.

user
\frac{99}{100}
What is the value of the sum $\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \cdots + \frac{1}{n(n+1)} +\cdots + \frac{1}{9900}$? Express your answer as a common fraction.
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