Lê Quốc Trần Anh Coordinator
13/07/2017 at 12:07-
V 13/07/2017 at 17:52\(\dfrac{1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{999}}{\dfrac{1}{1.999}+\dfrac{1}{3.997}+...+\dfrac{1}{997.3}+\dfrac{1}{999.1}}\)
\(=\dfrac{\left(1+\dfrac{1}{999}\right)+\left(\dfrac{1}{3}+\dfrac{1}{997}\right)+...+\left(\dfrac{1}{499}+\dfrac{1}{501}\right)}{2\left(\dfrac{1}{1.999}+\dfrac{1}{3.997}+...+\dfrac{1}{499.501}\right)}\)
\(=\dfrac{\dfrac{1000}{1.999}+\dfrac{1000}{3.997}+...+\dfrac{1000}{499.501}}{2\left(\dfrac{1}{1.999}+\dfrac{1}{3.997}+...+\dfrac{1}{499.501}\right)}\)
\(=\dfrac{1000\left(\dfrac{1}{1.999}+\dfrac{1}{3.997}+...+\dfrac{1}{499.501}\right)}{2\left(\dfrac{1}{1.999}+\dfrac{1}{3.997}+...+\dfrac{1}{499.501}\right)}\)
\(=\dfrac{1000}{2}=500\)
Lê Quốc Trần Anh selected this answer. -
FA KAKALOTS 28/01/2018 at 22:141+13+15+...+199911.999+13.997+...+1997.3+1999.1
=(1+1999)+(13+1997)+...+(1499+1501)2(11.999+13.997+...+1499.501)
=10001.999+10003.997+...+1000499.5012(11.999+13.997+...+1499.501)
=1000(11.999+13.997+...+1499.501)2(11.999+13.997+...+1499.501)
=10002=500