If ,\(\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot...\cdot\frac{n}{n+1} = \frac{1}{50}\) what is the sum of the numerator and denominator of the largest fraction on the left side of the equation?
+128460 Note that in all the fractions, the denominator of the previous fraction will "cancel" the numerator of the next
So at the end we will have this left
2 1
_______ = ___ cross-multiply
n + 1 50
50 (2) = 1 ( n + 1)
100 = n + 1 subtract 1 from both sides
99 = n
n + 1 = 100
So....the sum of n , n + 1 = 199
+2094 Here is another answer, even though I'm not one of the "awesome people>"
Since all of these cross out, we're left with
2/(n+1)=1/50.
Therefore, the number has to be 1/100, making n+1 100.
Therefore, n=100,
100+99=199.
Hope this helped!
