MathDB

Let

f(x)=\frac{\sin x}{x}

, for

x>0

, and let

n

be a positive integer. Prove that

|f^{(n)}(x)|<\frac{1}{n+1}

, where

f^{(n)}

denotes the

n^{\mathrm{th}}

derivative of

f

.
(Proposed by Alexander Bolbot, State University, Novosibirsk)

Problem Statement