SOLUTION: Simplify the expression (1 - 1/2)(1 - 1/3)(1 - 1/4)... ... ... ... (1 - 1/n), where n is a positive integer.
I have no idea where to begin with this. Could you please help me??
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I have no idea where to begin with this. Could you please help me??
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Question 675285: Simplify the expression (1 - 1/2)(1 - 1/3)(1 - 1/4)... ... ... ... (1 - 1/n), where n is a positive integer.
I have no idea where to begin with this. Could you please help me??
Thank you! Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! I can write this as
( 1/2 )*( 2/3 )*( 3/4 )*( 4/5 )* . . . ( n-2)/( n-1 )*( n-1 )/( n )
There are cancellations on the top and bottom
I can rewrite the whole thing as
(2/2)*(3/3)*4/4)* . . . (n-1)/(n-1) * (1/n)
This equals 1/n
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You can test it for n = 5, for instance
( 1/2)*(2/3)*(3/4)*(4/5) =
(2/2)*(3/3)*(4/4)*(1/5) = 1/5
