- #1
stanleyman
- 2
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Homework Statement
Determine which row of pascals triangle contains 3 consecutive entries that are in the ratio 1:2:3.
Homework Equations
(n, k ) = n!/k!(n-k)!
The Attempt at a Solution
(n,k):(n,k+1):(n,k+2)
1 : 2: : 3
What I did was cross multiply.
2 times (n,k) = 1 times (n,k+1) and 3 times (n,k+1) = 2 times (n,k+2)
2(n!/(k!(n-k)!) = n!/(k+1)!(n-k-1)! and 3(n!/(k+1)!(n-k-1)!) = 2(n!/(k+2)!(n-k-2)!
I know that i should solve for n in the first equation then substitute n in the second equation to get n and k. I'm stuck on the algebra part.