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There is a sequence ni such, in which i is a positive intege

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by Max@Math Revolution » Mon Mar 21, 2016 3:30 am
There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n21?

A. 100~1,000
B. 1,000~10,000
C. 10,000~100,000
D. 100,000~1,000,000
E. 1,000,000~


* A solution will be posted in two days.
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by ratanvk » Mon Mar 21, 2016 5:42 am
Ans E
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by Max@Math Revolution » Tue Mar 22, 2016 5:01 pm
There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n21?

A. 100~1,000
B. 1,000~10,000
C. 10,000~100,000
D. 100,000~1,000,000
E. 1,000,000~


-> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n21=2^20=(2^10)^2>(10^3)^2=10^6
Thus, the answer is E.
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