SOLUTION: What is the product of the first 99 products in the sequence 1/2 2/3 3/4 4/5...?
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Question 25077: What is the product of the first 99 products in the sequence 1/2 2/3 3/4 4/5...?
Found 2 solutions by venugopalramana, askmemath:
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
WE HAVE 1/2*2/3*3/4*......*99/100
2,3,4,...TILL 99..IN NUMERATOR AND DENOMINATOR CANCEL EACH OTHER .SO WE GET
ANSWER AS 1/100
Answer by askmemath(368) (Show Source): You can put this solution on YOUR website!
Consider only the first 2 terms
The 2 in the Numerator and Denominator cancel leaving you with only
Expand this to 3 terms
The 2 and 3 will cancel leaving you out with
You will observe that as we increase the number of terms, the denominator increases by 1 everytime
So for 99 terms the denominator increasing by 1 will give us 100
And so your answer will be
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