Đặt: \(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2011.2013}\)

\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2011.2013}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2011}-\frac{1}{2013}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{2013}\right)\)

\(=\frac{1}{2}.\frac{2012}{2013}\)

\(=\frac{1006}{2013}\)

a, 3/22 x 3/11 x 22

Cách 1

  3/22 x 3/11 x 22 = 9/242 x 22

                            = 198/242

                            = 9/11

Cách 2

3/22 x 3/11 x 22 = 3 x 3 x 22/22 x 11 x 1

                          = 9/11

b,( 1/2 + 1/3) x 2/5

Cách 1

( 1/2 + 1/3 ) x 2/5 = 5/6 x 2/5

                            = 10/30

                            = 1/3

Cách 2

( 1/2  +1/3) x 2/5 = 1/2 x 2/5 + 1/3 x 2/5

                           = 2/10  +  2/15

                           = 1/5  +  2/15

                           = 3/15  +  2/15

                           = 5/15

                           = 1/3

c, 3/5 x 17/21 + 17/21 x 2/5

Cách 1

3/5 x 17/21 + 17/21 x 2/5 = 51/105 + 34/105

                                        = 85/105

                                        =  17/21          

Cách 2

3/5 x 17/21 + 17/21 x 2/5 = 17/21 x (3/5 +2/5)

                                         = 17/21 x 5/5

                                         = 17/21 x 1

                                         = 17/21

 HỌC TỐT ( k mk nhé)

\(A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{18.19.20}\)

\(2A=\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{20-18}{18.19.20}=\)

\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{18.19}-\dfrac{1}{19.20}=\dfrac{1}{2}-\dfrac{1}{19.20}\)

\(\Rightarrow A=\left(\dfrac{1}{2}-\dfrac{1}{19.20}\right):2\)

Đề bài yêu cầu j vậy?

mũ 2 tui ko bt

chịu bạn ơi

Các bạn giúp mình giải nhớ chi tiết một tí nhé!

a)

 \(\begin{array}{l}M = \frac{1}{7}.(\frac{{ - 5}}{8}) + \frac{1}{7}.(\frac{{ - 11}}{8})\\ = \frac{{ - 5}}{{56}} + \frac{{ - 11}}{{56}} = \frac{{ - 16}}{{56}} = \frac{{ - 2}}{7}\end{array}\)

b)

\(\begin{array}{l}M = \frac{1}{7}.(\frac{{ - 5}}{8}) + \frac{1}{7}.(\frac{{ - 11}}{8})\\ = \frac{1}{7}.[(\frac{{ - 5}}{8}) + (\frac{{ - 11}}{8})]\\ = \frac{1}{7}.\frac{{ - 16}}{8}\\ = \frac{1}{7}.( - 2)\\ = \frac{{ - 2}}{7}\end{array}\)

a) =B3*1+C3*1+D3*2+B3*3/7

b) =H5^2*H6+10

c) =A3+B3+C3+C3+C3/5