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What is the value of (1 - 122)(1 - 132)(1 - 142)….(1 - 1202)?

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What is the value of (1 - 122)(1 - 132)(1 - 142)….(1 - 1202)?

by Max@Math Revolution » Tue Jul 14, 2020 12:17 am

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[GMAT math practice question]

What is the value of (1 - 1/2^2)(1 - 1/3^2)(1 - 1/4^2)….(1 - 1/20^2)?

A. 11/10
B. 20/39
C. 21/40
D. 23/41
E. 27/50
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Re: What is the value of (1 - 122)(1 - 132)(1 - 142)….(1 - 1202)?

by Max@Math Revolution » Wed Jul 15, 2020 11:31 pm
=>

(1 - 1/2^2)(1 - 1/3^2)(1 - 1/4^2)….(1 - 1/20^2)?
= (1 + 1/2)(1 - 1/2)(1 + 1/3)(1 - 1/3)(1 + 1/4)(1 - 1/4)….(1 + 1/20)(1 - 1/20)
= (1 + 1/2)(1 + 1/3)(1 + 1/4)…(1 + 1/20)(1 - 1/2)(1 - 1/3)(1 - 1/4)…(1 - 1/20)
= (3/2*4/3*5/4*21/20) (1/2*2/3*3/4*19/20)
= 21/2*1/20
= 21/40

Therefore, C is the correct answer.
Answer: C
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