SOLUTION: Given that a/b = 1- 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 - 1/10 , such that a and b have no common divisor greater than 1, find the value of a.

Question 1137875: Given that
a/b = 1- 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 - 1/10
, such that a and b have no common divisor greater than 1, find the value of a.
Answer by ikleyn(52814) (Show Source): You can put this solution on YOUR website!
.

    1- 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 - 1/10 = 


= (10! - 10!/2 + 10!/3 - 10!/4 + 10!/5 - 10!/6 + 10!/7 - 10!/8 + 10!/9 - 10!/10)/10! =  


    = (the following value of the numerator is calculated using Excel) = 


= 2342880/(1*2*3*4*5*6*7*8*9*10) = .


The value of " a " = 1627.      ANSWER.     (the value of  " b " = 2520)



CHECK.  The sum  1- 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 - 1/10   calculated with Excel is  0.645635.


        The ratio   =  = 0.645635  is PRECISELY THE SAME value.

Solved, answered, explained and completed.

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