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(1/33)+(1/34)+ . . . +(1/63)+(1/64)

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(1/33)+(1/34)+ . . . +(1/63)+(1/64)

by M7MBA » Sun Oct 29, 2017 7:29 am
(1/33)+(1/34)+ . . . +(1/63)+(1/64) is including in which of the following ranges?

A. (1/6)~(1/5)
B. (1/5)~(1/4)
C. (1/4)~(1/3)
D. (1/3)~(1/2)
E. (1/2)~1

The OA is E.

How could I determine the correct range? Experts, I don't know how to solve it.
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by ceilidh.erickson » Sun Oct 29, 2017 11:34 am
The key is that this question is asking you for the RANGE that the answer falls in - it's not actually asking you to calculate. You definitely should not try to actually calculate! That would take far too much time.

Instead, find a good way to approximate. If we go from 33 to 64, that's 32 terms (64 - 33 + 1).

First, image that we were adding 1/32 + 1/32 + 1/32.... 32 times. That would add up to 1. Since all of our terms are smaller than 1/32, we know that the sum is less than 1.

Now, imagine that all 32 terms were 1/64. (32)(1/64) would give us 1/2. Since all but the last term is actually greater than 1/64, we know that the overall sum must be greater than 1/2.

Using that reasoning, the only answer that makes sense is E.
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by ceilidh.erickson » Sun Oct 29, 2017 11:36 am
By the way, this question is very similar in structure to this OG question: https://www.beatthegmat.com/m-is-the-sum ... tml#793900
See if you can try it without calculating!

Please POST THE SOURCE of your question - it's a copyright violation not to do so!
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by ceilidh.erickson » Sat Nov 18, 2017 1:05 pm
M7MBA, following up.

What was the source of this question?
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