1992 AIME Problems/Problem 4
In Pascal's Triangle, each entry is the sum of the two entries above it. In which row of Pascal's Triangle do three consecutive entries occur that are in the ratio ?
In Pascal's Triangle, we know that the binomial coefficients of the nth row are $\displaystyle n\chose 0$ (Error compiling LaTeX. ! Undefined control sequence.), ,...,. Let our row be the nth row such that the three consecutive entries are , , and .
After expanding and dividing one entry by another (to clean up the factorials), we see that and . Solving,