giả sử a = 22018 ; b = 32019 ; c = 52020
khi đó A = a/(a + b) + b/(b + c) + c/(c + a)
A > a/(a + b + c) + b/(a + b + c) + c/(a + b + c)
A > (a + b + c)/(a + b + c)
A > 1
ta có B = 1/(1 . 2) + 1/(3 . 4) + 1/(5 . 6) + ... + 1/(2019 . 2020)
2B = 2/(1 . 2) + 2/(3 . 4) + 2/(5 . 6) + ... + 2/(2019 . 2020)
Ta có dạng tổng quát sau 2/[k/(k + 1)] < 1/[(k - 1)k] + 1/[k(k + 1)]
khi đó 2B < 1/(1 . 2) + 1/(1 . 2) + 1/(2 . 3) + 1/(3 . 4) + ... + 1/(2018 . 2019) + 1/(2019 . 2020)
2B < 1/2 + 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2018 - 1/2019 + 1/2019 - 1/2020
2B < 1/2 + 1 - 1/2020
2B < 3/2 - 1/2020
B < 3/4 - 1/4040
B < 1
do đó A > B