2

Part of 2018 PUMaC Algebra A

Problems(1)

2018 PUMaC Algebra A2

Source:

a_1, a_2, \ldots

is a sequence of real numbers such that for all

n

\sum_{k = 1}^n a_k \left( \frac{k}{n} \right)^2 = 1,

find the smallest

n

a_n < \frac{1}{2018}