Question

$1/(2 \times 3) + 1/(3 \times 4) + ... + 1/(49 \times 50) = ?$

• A. 12/25
• B. 8/25
• C. 29/50
• D. 47/50

Hint:

In a series of $\frac{1}{n(n+1)}$, the result is $\frac{1}{\text{first}} - \frac{1}{\text{last}}$.

Answer 1

The Correct Option is A

Step 1: Concept
Telescoping Series.

Step 2: Analysis
Each term $\frac{1}{n(n+1)}$ can be written as $(\frac{1}{n} - \frac{1}{n+1})$.

Step 3: Calculation
$(\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + ... + (\frac{1}{49} - \frac{1}{50})$.
All middle terms cancel out, leaving $\frac{1}{2} - \frac{1}{50}$.
Sum = $\frac{25 - 1}{50} = \frac{24}{50} = \frac{12}{25}$.

Step 4: Conclusion
The sum is 12/25. Final Answer: (A)