ta có:

C = 1 - 1/3 + 1/3 - 1/5 +...+1/69 - 1/71 + 1/71 - 1/73

    = 1 - 1/ 73

    = 72/73

\(C=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{69.71}+\)\(\frac{2}{71.73}\)

\(C=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{69}-\frac{1}{71}+\frac{1}{71}-\frac{1}{73}\)

\(C=1-\frac{1}{73}\)

\(C=\frac{72}{73}\)

c) C = 1 - 1/3 + 1/3 - 1/5 + ... + 1/71 - 1/73

        = 1 - 1/73

        = 72/73

ủng hộ mk nha!

Tính :

a) \(M=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{100}{101}\)

b) \(A=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

\(=7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)

\(=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(=7.\left(\frac{1}{10}-\frac{1}{70}\right)\)

\(=7.\frac{3}{35}\)

\(=\frac{3}{5}\)

c) \(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)

\(=\frac{1}{2}.\left(\frac{2}{25.27}+\frac{2}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{75}\right)\)

\(=\frac{1}{2}.\frac{2}{75}\)

\(=\frac{1}{75}\)

thanks

M=2/1.3+2/3.5+2/5.7+...+2/99.101

    =1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101

    =1-1/101

    =101/101-1/101

 M = 99/101

A=7/10.11+7/11.12+7/12+13+7/69/70 ( sai đề )

 B= 1/25.27+1/27.29+1/29.31+...+1/73.75

   =1/2.(2/25.27+2/27.29+2/29.31+...+2/73.75

   =1/2.(1/25-1/27+1/27-1/29+1/29-1/31+...+1/73-1/75

   =1/2.(1/25-1/75)

   =1/2.75/100

   =3/8

a)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}=\left(1-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{7}\right)+...+\left(\frac{1}{99}-\frac{1}{101}\right)\)

                                                               \(=1-\frac{1}{101}=\frac{100}{101}\)

b) \(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{99.101}=\frac{2}{1.3}.\frac{5}{2}+\frac{2}{3.5}.\frac{5}{2}+\frac{2}{5.7}.\frac{5}{2}+...+\frac{2}{99.101}.\frac{5}{2}\)

                                                                \(=\frac{5}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

                                                                \(=\frac{5}{2}.\frac{100}{101}=\frac{250}{101}\)

a)100/101

b)250/101

A)100/101

B)250/101

a.2/1.3+2/3.5+2/5.7+................+2/99.101

1-1/3+1/3-1/5+1/5-1/7+....+1/99-1/101

1-1/101

100/101

b.5/1.3+5/3.5+5/5.7+............+5/99.101

5.2/1.3.2+5.2/3.5.2+5.2/5.7.2+........+5.2+99.101.2

5/2(2/1.3+2/3.5+2/5.7+........+2/99.101)

5/2(1-1/3+1/3-1/5+1/5-1/7+........+1/99-1/101)

5/2(1-1/101)

5/2.100/101

250/101

còn cần không bạn, mk làm cho

\(A=\) \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(A=1-\frac{1}{50}\)

\(A=\frac{49}{50}\)

\(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.50}\)

A= \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\)

A = \(\frac{1}{1}-\frac{1}{51}=\frac{50}{51}\)

làm dài lắm,nếu muốn thì k minh còn ko thì thôi

a,0,36.350+1,2.20.3+9.4.4,5

=13.3.35+12.2.3+9.2.3.3

=3.(13.35+12.2+.9.2.3)

=3.(455+24+54)

=3.533

=1599

b,2015.2016-5/2015.2015+2010

=4062240-5+2010

=4064245

c,2/1.3+2/3.5+2/5.7+...+2/71.73

=1-1/3+1/3-1/5+1/5-1/7+...+1/71-1/73

=1-1/73

=72/73

d,(1+1/2).(1+1/3)+...+(1+1/2018)

=3/2.4/3.5/4+...+2019/2018

=2019/2

e,E=1/4.5+1/5.6+1/6.7+...+1/80.81(làm tương tự với phần d nên mình làm ngắn

     =1/4-1/81

     =77/324

f,F=3/2.3+3/3.4+...+3/99.100

=3.(1/2.3+1/3.4+...+1/99.100)(làm tương tự với d

=3.(1/2-1/100)

=3.49/100

=147/100

gG=5/1.4+5/4.7+...+5/61.64

3G=5.(3/1.4+3./4.7+...+3/61.64)

     =5.(1-1/64)

     =5.63/64

     =315/64

ok nha bạn,mình giữ đúng lời hứa.

\(B=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+..+\frac{1}{55}\)

\(B=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{110}\)

\(B=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{10.11}\)

\(B=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(B=2.\left(\frac{1}{2}-\frac{1}{11}\right)=2.\frac{9}{22}=\frac{9}{11}\)

làm cả 3 nhé 

bạn do not ask why làm sai ở bước 4 rồi 

a) =1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101

    =1-1/101

    =100/101

b) =(2/1.3+2/3.5+2/5.7+...+2/99.101).2,5

    =(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101).2,5

    =(1-1/101).2,5

    =100/101.2,5

    =250/101

c) =(2/2.4+2/4.6+2/6.8+...+2/2008-2/2010).2

    =(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2008-1/2010).2

    =(1/2-1/2010).2

    =1004/1005

=1-1/3+1/3-1/5+...+1/2015-1/2017

=1-1/2017

=2016/2017