ABC26GN0737 · Decimal Fractions
Subject: General Aptitude · Chapter: Decimal Fractions · Exam: · Marks: · Difficulty:
The sum of the first 20 terms of the series $\frac{1}{5 \times 6}+\frac{1}{6 \times 7}+\frac{1}{7 \times 8}+\ldots .$. is
(a)0.16
(b)1.6
(c)16
(d)None of these
Answer
Explanation
Given expression $=\frac{1}{5 \times 6}+\frac{1}{6 \times 7}+\frac{1}{7 \times 8}+\ldots . .+\frac{1}{24 \times 25}$ $$\begin{aligned} & =\left(\frac{1}{5}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)+\left(\frac{1}{7}-\frac{1}{8}\right)+\ldots .+\left(\frac{1}{24}-\frac{1}{25}\right) \\ & =\left(\frac{1}{5}-\frac{1}{25}\right)=\frac{4}{25}=0.16 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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