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If 2/3*3/4*4/5*...*n/(n+1)=1/500, what is the sum of the numerator and denominator of the largest fraction on the left side of the equation?

 Apr 18, 2022

Best Answer 

 #1
avatar+23183 
+1

2/3 x 3/4 x 4/5 x 5/6 x ... x n/(n + 1)  =  1 / 500

 

Notice that the denominator of the first fraction cancels the numerator of the second fraction and this pattern continues throughtout.

 

So, the only numbers left on the left-hand-side are 2 and n + 1.

 

This means that 2 / (n + 1)  =  1 / 500     --->     1000  =  n + 1     --->    n  = 999

So:  n / (n + 1)  =  999 / 1000

 Apr 18, 2022
 #1
avatar+23183 
+1
Best Answer

2/3 x 3/4 x 4/5 x 5/6 x ... x n/(n + 1)  =  1 / 500

 

Notice that the denominator of the first fraction cancels the numerator of the second fraction and this pattern continues throughtout.

 

So, the only numbers left on the left-hand-side are 2 and n + 1.

 

This means that 2 / (n + 1)  =  1 / 500     --->     1000  =  n + 1     --->    n  = 999

So:  n / (n + 1)  =  999 / 1000

geno3141 Apr 18, 2022
 #2
avatar+122 
-3

Correct

sincerely▄︻デ🇮‌🇫‌1️⃣🇳‌1️⃣🇹‌¥══━一

 Apr 18, 2022

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