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If A = (1+1/3)(1+1/3^2)(1+1/3^4)(1+1/3^8), what is 1 - 2/3A?

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If A = (1+1/3)(1+1/3^2)(1+1/3^4)(1+1/3^8), what is 1 - 2/3A?

by Max@Math Revolution » Wed Mar 18, 2020 2:46 am

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[GMAT math practice question]

If A = (1+1/3)(1+1/3^2)(1+1/3^4)(1+1/3^8), what is 1 - 2/3A?

A. 1/3
B. 2/3^2
C. 2/3^4
D. 2/3^8
E. 1/3^16
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Re: If A = (1+1/3)(1+1/3^2)(1+1/3^4)(1+1/3^8), what is 1 - 2/3A?

by Max@Math Revolution » Sun Mar 22, 2020 6:50 pm
=>

(2/3)A=(1-1/3)A=(1-1/3)(1+1/3)(1+1/3^2)(1+1/3^4)(1+1/3^8)
= (1-1/3^2)(1+1/3^2)(1+1/3^4)(1+1/3^8)
= (1-1/3^4)(1+1/3^4)(1+1/3^8)
= (1-1/3^8)(1+1/3^8)
= (1-1/3^16)

Then, we have 1-2/3A=1-1-1/3^16= 1/3^16

Therefore, the answer is E.
Answer: E
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