Sequences (an),(bn) are defined by a1=1,b1=2, an+1=1+an+anbnbn, bn+1=1+bn+anbnan for all positive integers n. Prove that a2020<5.
Source: 2020 Latvia TST Round 1
Tags: algebra
Sequences (an),(bn) are defined by a1=1,b1=2, an+1=1+an+anbnbn, bn+1=1+bn+anbnan for all positive integers n. Prove that a2020<5.