Question Bank › General Aptitude › Simplification › ABC26GN1072ABC26GN1072 · Simplification Subject: General Aptitude · Chapter: Simplification · Exam: · Marks: · Difficulty:
The value of $\left(1-\frac{1}{3^{2}}\right)\left(1-\frac{1}{4^{2}}\right)\left(1-\frac{1}{5^{2}}\right) \ldots\left(1-\frac{1}{11^{2}}\right)$ $\left(1-\frac{1}{12^{2}}\right)$ is
(a) $\frac{11}{20}$
(b) $\frac{13}{15}$
(c) $\frac{13}{18}$
(d) $\frac{15}{16}$
(e) None of these
Answer Explanation Given exp. $=\left(\frac{3^{2}-1}{3^{2}}\right)\left(\frac{4^{2}-1}{4^{2}}\right)\left(\frac{5^{2}-1}{5^{2}}\right)\ldots\left(\frac{11^{2}-1}{11^{2}}\right)\left(\frac{12^{2}-1}{12^{2}}\right) = \left[\frac{(3+1)(3-1)}{(2+1)(4-1)}\right]\left[\frac{(4+1)(4-1)}{(3+1)(5-1)}\right]\left[\frac{(5+1)(5-1)}{(4+1)(6-1)}\right]\ldots\left[\frac{(11+1)(11-1)}{(10+1)(12-1)}\right]\left[\frac{(12+1)(12-1)}{(11+1)(13-1)}\right] = \frac{(3-1)(12+1)}{(2+1)(13-1)} = \frac{2}{3} \times \frac{13}{12} = \frac{13}{18}$.
Explanation as extracted from the printed page; notation may be imperfect.
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