WBJEE · Maths · Sequences and Series
The value of \(1000\left[\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+\ldots+\frac{1}{999 \times 1000}\right]\) is
- A 1000
- B 999
- C 1001
- D \(\frac{1}{999}\)
Answer & Solution
Correct Answer
(B) 999
Step-by-step Solution
Detailed explanation
\(1000\left[\frac{1}{1 \times 2} \times \frac{1}{2 \times 3}+\frac{1}{3 \times 4}+\ldots+\frac{1}{999 \times 1000}\right]\) \(=1000\left\{\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)\right.\)…
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