GATE 2015 CS – Question 41
$\sum_{x=1}^{99} \frac{1}{x(x+1)} =$ ________.
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Correct answer: 0.98 to 1.00
Explanation
Split each term as $\frac{1}{x(x+1)} = \frac{1}{x} - \frac{1}{x+1}$. The sum telescopes, leaving $1 - \frac{1}{100} = 0.99$.