Nguyễn Đức Anh's Profile

cho tam giac abc,B=20+c,C=20+a.tinh A,B,C

Ta thấy :

12!=11.2=1−122!1​=1.21​=1−21​

13!=11.2.3=12.3=12−133!1​=1.2.31​=2.31​=21​−31​

14!=11.2.3.4<13.4=13−144!1​=1.2.3.41​<3.41​=31​−41​

$............$

1100!=11.2.3...99.100<199.100=199−1100100!1​=1.2.3...99.1001​<99.1001​=991​−1001​

Cộng vế với vế ta được :

12!+13!+14!+....+1100!<1−12+12−13+...+199−1100=1−1100<12!1​+3!1​+4!1​+....+100!1​<1−21​+21​−31​+...+991​−1001​=1−1001​<1

Vậy 12!+13!+14!+....+1100!<12!1​+3!1​+4!1​+....+100!1​<1 (đpcm)