Let z0 ă z1 ă z2 ă ¨ ¨ ¨ be an infinite sequence of...

Let z0 ă z1 ă z2 ă ¨ ¨ ¨ be an infinite sequence of positive integers. Prove that there
exists a unique integer n ě 1 such that
zn ă
z0 ` z1 ` ¨ ¨ ¨ ` zn
n
ď zn`1.?

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