1,Tính
a, A = \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + . . . + \(\dfrac{1}{2017.2018}\)
b,B = \(\dfrac{5}{2.4}\) + \(\dfrac{5}{4.6}\) + \(\dfrac{5}{6.8}\) + . . . + \(\dfrac{5}{2016.2018}\)
c. C = \(\dfrac{1}{18}\) + \(\dfrac{1}{54}\) + \(\dfrac{1}{108}\) + . . . + \(\dfrac{1}{990}\)
a, A = 1 - 1/2 + 1/2 - 1/3 + 1/3 -1/4 +... + 1/2017 - 1/2018
A = 1 - 1/2018 = 2017/2018
b, B = 5/2 . ( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/2016 -1/2018)
B= 5/2 . ( 1/2 - 1/ 2018 )
B = 504/1009
c, C = 1/3.6 + 1/ 6.9 + 1/ 9.12 + ... + 1/ 30.33
C= 1/3 - 1/6 + 1/6 - 1/ 9 + 1/9 - 1/12 + ... + 1/30 - 1/33
C = 1/3 - 1/33
C= 10/33
phan B mk quên nhân với 5/2
lấy 5/2 . 504/1009 = 1260/1009
a) \(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2017.2018}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2017}-\dfrac{1}{2018}\)
\(=1-\dfrac{1}{2018}=\dfrac{2017}{2018}.\)
b) \(B=\dfrac{5}{2.4}+\dfrac{5}{4.6}+\dfrac{5}{6.8}+...+\dfrac{5}{2016.2018}\)
\(=2,5\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{2016.2018}\right)\)
\(=2,5\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2016}-\dfrac{1}{2018}\right)\)
\(=2,5\left(\dfrac{1}{2}-\dfrac{1}{2018}\right)=\dfrac{1260}{1009}.\)
c) \(C=\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{108}+...+\dfrac{1}{990}\)
=>\(3C=\dfrac{3}{3.6}+\dfrac{3}{6.9}+\dfrac{3}{9.12}+...+\dfrac{1}{30.33}\)
\(=\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{30}-\dfrac{1}{33}\)
\(=\dfrac{1}{3}-\dfrac{1}{33}=\dfrac{10}{33}\)
=> \(C=\dfrac{10}{33}:3=\dfrac{10}{99}.\)
a. A=\(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+.....+\(\dfrac{1}{2017.2018}\)
A= 1-\(\dfrac{1}{2}\)+ \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) +. . .+\(\dfrac{1}{2017}\) -\(\dfrac{1}{2018}\)
A=1-\(\dfrac{1}{2018}\)
A=\(\dfrac{2018}{2018}\)-\(\dfrac{1}{2018}\)
A=\(\dfrac{2017}{2018}\)
