Pascals triangle problem(discrete mathematics)

[stanleyman]

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.

 

[Mentallic]

Well, what are some of the rules of factorials?

n! = n*(n-1)*(n-2)*...*2*1

n! = n*(n-1)!

So if we have an equation such as

n! = 10*(n-1)!

then to solve this, we would use the rule n! = n*(n-1)! to obtain

n*(n-1)! = 10*(n-1)!

then you can divide through by (n-1)! and find n=10. See if you can apply this rule to solve your equation.

 

[stanleyman]

thank you i got the answer.