Allied & ICAR Exam Bank • ALLIED_2662 NAT • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Sequences and series – infinite series, tests for convergence

Question Statement:

The value of the infinite sum $\sum_{n=1}^\infty \frac{1}{n(n+1)} = \left(1 - \frac{1}{2}\right) + \left(\frac{1}{2} - \frac{1}{3}\right) + \dots$ is:

Answer Key:

1

Step-by-Step Solution & Explanation

Telescoping series: $S_N = 1 - \frac{1}{N+1}$. As $N \to \infty$, $S = 1$.
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