SOLUTION: P = (1 - 1/2)(1 - 1/3)(1 - 1/4)...(1 - 1/16) The three dots in the product above represent eleven missing factors of the form (1 - 1/n), where n represents all of the consecutive

Question 279700: P = (1 - 1/2)(1 - 1/3)(1 - 1/4)...(1 - 1/16)
The three dots in the product above represent eleven missing factors of the form (1 - 1/n), where n represents all of the consecutive integers from 5 to 15, inclusive. What is P equal to?
a. 1/16
b. 1/2
c. 7/8
d. 15/16
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
P = (1 - 1/2)(1 - 1/3)(1 - 1/4)...(1 - 1/16)
The three dots in the product above represent eleven missing factors of the form (1 - 1/n), where n represents all of the consecutive integers from 5 to 15, inclusive. What is P equal to?
a. 1/16
b. 1/2
c. 7/8
d. 15/16
P = (1 - 1/2)(1 - 1/3)(1 - 1/4)...(1 - 1/16)
P = 1/1 * 1/2 * 2/3 * 3/4 * ... * 15/16
so in numerator you have product of 1 through 15 times 1 which is still product of 1 through 15
and in denominator you have product of through 16
or P = 15! / 16!
the 15! on top and bottom cancel out leaving
P = 1/16
so answer is A. 1/16

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