Find the smallest value of n such that Row n of Pascal's Triangle contains three successive entries with the ratio 3:4:5.

You need to solve the following two equations

 

nCr(n,k)/nCr(n,k+1) = 3/4

nCr(n,k+1)/nCr(n,k+2) = 4/5

 

Unfortunately, the calculator on the home page here doesn't seem to be able to solve these simultaneously.  

The result I got using different software was n = 62 (and k = 26).

 

The calculator here will calculate nCr(62,26)/nCr(62,27)   and  nCr(62,27)/nCr(62,28) though.

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