Cho :
A= \(\dfrac{1}{1.2}+\dfrac{1}{3.4}+...+\dfrac{1}{2007.2008}+\dfrac{1}{2009}\)
B = \(\dfrac{1}{1005.2009}+\dfrac{1}{2006.2008}+...+\dfrac{1}{2009.1005}\)
Chứng minh : A = 1507 . B
Bài 1: Cho A=\(\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\)
a) Chứng minh: A=\(\dfrac{1}{51}+\dfrac{1}{52}+\dfrac{1}{53}+...+\dfrac{1}{100}\)
b) Chứng minh: A<\(\dfrac{5}{6}\)
1. Tính:
a.\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\)
b.\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)
2. Tìm x , biết:
a. \(\dfrac{2}{5}+\dfrac{4}{5}x-\dfrac{7}{5}=\dfrac{9}{5}\)
b. \(\dfrac{2}{5}x-\dfrac{6}{4}=\dfrac{8}{5}\)
bài này ko được coppy trên mạng
Chứng minh :
\(\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+...+\dfrac{1}{60}=\dfrac{1}{1.2}+\dfrac{1}{3.4}+..+\dfrac{1}{59.60}\)
Bài 1: Cho M= \(\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}\)+...+\(\dfrac{1}{50}\)
Chứng minh M = \(\dfrac{1}{26}+\dfrac{1}{27}+\dfrac{1}{28}+...+\dfrac{1}{50}\)
MÌNH CẢM ƠN ĐÃ GIÚP CHO MÌNH~
BT2: Tìm x, biết
1) \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{x.\left(x+1\right)}=\dfrac{2016}{2017}\)
Cho :
A = 1.2 .3 ....2017.2018 . ( 1 + \(\dfrac{1}{2}+\dfrac{1}{3}+.....+\dfrac{1}{2017}+\dfrac{1}{2018}\) )
CM : A\(\in\) N
A \(⋮\) 2019
BT1: Tính
5) \(\dfrac{1}{1+\dfrac{2009}{2011}+\dfrac{2009}{2010}}+\dfrac{1}{1+\dfrac{2010}{2009}+\dfrac{2010}{2011}}+\dfrac{1}{1+\dfrac{2011}{2009}+\dfrac{2011}{2010}}\)
Cho :
A = \(\dfrac{1}{2.17}+\dfrac{1}{3.18}+\dfrac{1}{4.19}+...+\dfrac{1}{1990.2005}\)
B = \(\dfrac{1}{2.1991}+\dfrac{1}{3.1992}+\dfrac{1}{4.1993}+...+\dfrac{1}{16.2005}\)
Chứng minh : \(\dfrac{A}{B}=\dfrac{663}{5}\)
