MathDB

Let

(a_n)_{n\geq 1}

be a sequence of positive real numbers in which

\lim_{n\to\infty} a_n = 0

such that there is a constant

c >0

so that for all

n \geq 1

|a_{n+1}-a_n| \leq c\cdot a_n^2

. Show that exists

d>0

with

na_n \geq d, \forall n \geq 1

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