A = 1.2 + 2.3 + 3.4 + ....... + 99.100
3A = 1.2.3 + 2.3.3 + 3.4.3 + ....... + 99 . 100 . 3
3A = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) +.... + 99.100.(101-98)
3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 99 . 100 . 101 - 98 . 99 . 100
3A = (1.2.3 - 1.2.3) + (2.3.4-2.3.4) + ... + (98.99.100 - 98.99.100) + 99 . 100 . 101
3A = 99 . 100 . 101 = 999900
A = 999900 : 3 = 343400

P/S: Chúc bạn hok tốt !!!

A= \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2018.2019}\)

A= 1 - \(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{2018}-\frac{1}{2019}\)

A= 1 - \(\frac{1}{2019}\)

A= \(\frac{2018}{2019}\)

\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{2018\cdot2019}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2018}-\frac{1}{2019}\)

\(A=1-\frac{1}{2019}\)

\(=\frac{2018}{2019}\)

Vậy \(A=\frac{2018}{2019}\)

HOK TỐT ==.==

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{2018.2019}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-.....-\frac{1}{2019}\)

\(\Rightarrow A=1-\frac{1}{2019}\)

\(\Rightarrow A=\frac{2019}{2019}-\frac{1}{2019}=\frac{2018}{2019}\)

Vậy A = \(\frac{2018}{2019}\)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2018+2019}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2018}-\frac{1}{2019}\)

=\(1-\frac{1}{2019}< 1\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2018.2019}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2018}-\frac{1}{2019}\)

\(A=\frac{1}{1}-\frac{1}{2019}< 1\)

Vậy \(A< 1\)

\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}+\frac{1}{2018.2019}\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}+\frac{1}{2018}-\frac{1}{2019}\)

( gạch bỏ các phân số giống nhau)

\(S=1-\frac{1}{2019}\)

\(S=\frac{2018}{2019}\)

CHÚC BN HỌC TỐT!!!!

S=1/1.2+1/2.3+1/3.4+............1/2017.2018+1/2018.2019

S=1/2.(1+1/3.2+1/3.2+.............1/2017.1009+1/1009.2019)

S=1/4.(2+2/3.2+2/3.2+..............2/2017.1009+2/1009.2019)

S=1/4.(1-1/2+1/2-1/3+1/3+..........+1/1009-1/1009+1/2019)

S=1/4.(1-1/2019)

S=1/4.2018/2019=1009/4038

S=1-1/2+1/2-1/3+1/3-1/4+.........+1/2017-1/2018+1/2018-1/2019

S=1-1/2019

S=2019/2019-1/2019

S=2018/2019

\(\text{#}HaimeeOkk\)

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{2018.2019}+\dfrac{1}{2019.2020}\)

\(A=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{2018}-\dfrac{1}{2019}+\dfrac{1}{2019}-\dfrac{1}{2020}\)

\(A=1-\left(\dfrac{1}{2}-\dfrac{1}{2}\right)-\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-\left(\dfrac{1}{4}-\dfrac{1}{4}\right)-...-\left(\dfrac{1}{2019}-\dfrac{1}{2019}\right)-\dfrac{1}{2020}\)

\(A=1-0-0-0-...-0-\dfrac{1}{2020}\)

\(A=1-\dfrac{1}{2020}\)

\(A=\dfrac{2019}{2020}\)

Vậy \(A=\dfrac{2019}{2020}\)

=3*(1/1.2+1/2.3+...+1/2018.2019)

=3(1-1/2+1/2-1/3+...+1/2018-1/2019)

=3(1-1/2019)

=3*2018/2019

=2018/673

\(A=\frac{3}{1.2}+\frac{3}{2.3}+...+\frac{3}{2018.2019}\)

  \(=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2018.2019}\right)\)

   \(=3.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2018}-\frac{1}{2019}\right)\)

    \(=3.\left(1-\frac{1}{2019}\right)\)

     \(=3.\frac{2018}{2019}=\frac{2018}{673}\)

à không, tính hoy nha

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2018.2019}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2018}-\frac{1}{2019}\)

\(=1-\frac{1}{2019}\)

\(=\frac{2018}{2019}\)

~Học tốt~

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2018.2109}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+...\frac{1}{2018}-\frac{1}{2019}\)

\(=1-\frac{1}{2019}\)

\(=\frac{2018}{2019}\)