6

Part of 2001 Putnam

Problems(2)

Source:

Can an arc of a parabola inside a circle of radius

1

have a length greater than

4

Putnamconicsparabolacollege contests

Source:

(a_n)_{n \ge 1}

is an increasing sequence of positive real numbers such that

\lim \tfrac{a_n}{n}=0

. Must there exist infinitely many positive integers

n

a_{n-i}+a_{n+i}<2a_n

i=1,2,\cdots,n-1

Putnamlimitcollege contests