SOLUTION: If S = (log 1/2) + (log 2/3) + (log 3/4) + ... + (log 998/999) + (log 999/1000), where the base of the logarithm is 10, what is the integral value of S in simplest form?

Question 1186901: If S = (log 1/2) + (log 2/3) + (log 3/4) + ... + (log 998/999) + (log 999/1000), where the base of the logarithm is 10, what is the integral value of S in simplest form?
Answer by ikleyn(52802) (Show Source): You can put this solution on YOUR website!
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If S = (log 1/2) + (log 2/3) + (log 3/4) + ... + (log 998/999) + (log 999/1000),


then  S = .


Now, in the global product, cancel the denominators and numerators in all neighbor fractions, and you will get simple expression


    S =  = -3.


THEREFORE, the final   A N S W E R   is  S = -3.

Solved.

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It is a kind of joke Math problem to entertain students at the end of the lesson . . .

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