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coolgirl26
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for every integer k..perplexing?
Source: Beat The GMAT — Problem Solving |
The above answer is absolutely correct, but geometric sums can be tricky, especially if you don't know the proper formulae. Attempting to derive the about result in two minutes would be fairly difficult.
Since the solutions do not require a specific answer, estimation is your best friend here. The sequence is 1/2 - 1/4 + 1/8 - 1/16 + 1/32... Each term becomes exponentially less relevant to the total.
After computing the sum of the first three terms (3/8), it should be clear that no single term after it is going to bring this sum below 2/8 or above 4/8, for obvious reasons. So you can pretty safely choose the correct answer.
Since the solutions do not require a specific answer, estimation is your best friend here. The sequence is 1/2 - 1/4 + 1/8 - 1/16 + 1/32... Each term becomes exponentially less relevant to the total.
After computing the sum of the first three terms (3/8), it should be clear that no single term after it is going to bring this sum below 2/8 or above 4/8, for obvious reasons. So you can pretty safely choose the correct answer.
I tutor GMAT/GRE level mathematics privately in the Los Angeles region, as well as via Skype for a discounted rate. Send me a message if you're interested.
