SSC CPO SI and ASI 2015 Paper

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Question : 131 of 199

Marks: +1, -0

When simplified, the product

\ (2-\ {1}/{3}\ ) (2-\ {3}/{5}\ )\ (2-\ {5}/{7}\ ) \..... (2 - {997}/{999}\ )

equals

5/999
5/3
1001/999
1001/3

Solution:

(4)

\ (2-\ {1}/{3} ) (2-\ {3}/{5}\ (2-\ {5}/{7}\ ) \........\ (2-\ {997}/{999} )

=\ (\ {6-1}/{3} (\ {10-3}/{5} (\ {14-5}/{7}\ )- (\ {1998-997}/{999}\ )

=\ {5}/{3} \×{7}/{5} ×{9}/{7} ×.............. ×{1001}/{999}= {1001}/{3}

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