Ratio of consecutive combinations for JEE

Formula

\(\dfrac{{}^nC_{r+1}}{{}^nC_r}=\dfrac{n-r}{r+1}\)

Variables: \(n\) is fixed, \(r\) varies.

Conditions: \(0\le r\le n-1\).

Finding greatest term/coefficient, monotonicity of binomial coefficients.