1.4

Part of 2019 Belarus Team Selection Test

Problems(1)

Inequality with a sequence

Source: 2019 Belarus Team Selection Test 1.4

Let the sequence

(a_n)

be constructed in the following way: a_1=1,\mbox{ }a_2=1,\mbox{ }a_{n+2}=a_{n+1}+\frac{1}{a_n},\mbox{ }n=1,2,\ldots. Prove that

a_{180}>19

inequalitiesalgebraSequences