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24 Jan 2005, 08:45
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Try this one guys:
If a = 1/2 * 3/4 * ... * 99/100, is a 1/10
If a = 1/2 * 3/4 * ... * 99/100, is a 1/10
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24 Jan 2005, 09:07
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B it is...
it seems the series in a keeps getting close to 1, but never quite reaches there...0.99 is as close it gets to 1...so we know the result of the multiplication is going to be way less than 1,
Statement 1) say b is between 0 and 1, which is what I expect series a to be...so therefor insufficient to tell if B > A.
Statement2) is clearly greater than 1/10 and we know that the series of A is less than 1/10. B is sufficient.
it seems the series in a keeps getting close to 1, but never quite reaches there...0.99 is as close it gets to 1...so we know the result of the multiplication is going to be way less than 1,
Statement 1) say b is between 0 and 1, which is what I expect series a to be...so therefor insufficient to tell if B > A.
Statement2) is clearly greater than 1/10 and we know that the series of A is less than 1/10. B is sufficient.
From i, we know the value of a but do not know the value of b. therefore, we can say a and b, both, are smaller than 1 and greater than 0 but we do not know which one is greater and which one is smaller.
from ii, the value of b is more than 1/10, and the value of a
a= 1/2*3/4=0.38
a= 1/2*3/4*5/6=0.31
a= 1/2*3/4*5/6*7/8=0.27
a= 1/2*3/4*5/6*7/8*9/10=0.25
a= 1/2*3/4*5/6*7/8*9/10*11/12=0.21
the value of a is in decreasing order. from the above simulation, we can generalize that a's value will decease as we add more terms. so, a will be less than 1/10. therfore it is safe to say b>a.
from ii, the value of b is more than 1/10, and the value of a
a= 1/2*3/4=0.38
a= 1/2*3/4*5/6=0.31
a= 1/2*3/4*5/6*7/8=0.27
a= 1/2*3/4*5/6*7/8*9/10=0.25
a= 1/2*3/4*5/6*7/8*9/10*11/12=0.21
the value of a is in decreasing order. from the above simulation, we can generalize that a's value will decease as we add more terms. so, a will be less than 1/10. therfore it is safe to say b>a.
& probably stop using Excel from now on!! Use your own Quant skills, will give more accurate results.
