let-m-N-and-0-lt-x-lt-m-if-i-m-1-x-x-1-prove-that-2-m-i-x-m-i-where-x-is-integer-part-of-x-and-m-i-is-a-binomial-coefficient-

Question Number 163718 by HongKing last updated on 09/Jan/22

let m \in N and 0 < x < m

if i = [\frac{(m + 1) x}{x + 1}]

prove that 2 (\begin{matrix} m \\ i \end{matrix}) ⩾ x^{m - i}

where [x] is integer part of x and (\begin{matrix} m \\ i \end{matrix})

is a binomial coefficient