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19 tháng 6 2015

A= 7/5*7 + 7/7*9 + ... + 7/53*55

A= 7/2*( 2/5*+ 2/7*9  +  ... + 2/53*55 )

A= 7/2*( 7-5/5*7 + 9-7/7*9 + ... + 55-53/53*55 )

A= 7/2*( 1/5-1/7 + 1/7-1/9 + ... + 1/53-1/55 )

A= 7/2*( 1/5-1/55 )

A= 7/2*2/11

A= 7/11

A= 7/11 > 1/2

 Nên: A > 1/2

 

B= 1/3 + 1/15 + 1/35 + ... + 1/99

B= 1/1*3 + 1/3*5 + 1/5*7 + ... + 1/9*11

B= 2*( 2/1*3 + 2/3*5 + 1/5*7 + ... + 2/9*11 )

B= 2*( 3-1/1*3 + 5-3/3*5 + 7-5/5*7 + ... + 11-9/9*11 )

B= 2*( 1/1-1/3 + 1/3-1/5 + 1/5-1/7 + ... + 1/9-1/11 )

B= 2*( 1/1-1/11 )

B= 2*10/11

B= 20/11

B= 20/11 < 1/2

Nên: B < 1/2

 

20 tháng 6 2015

A= 7/5*7 + 7/7*9 + ... + 7/53*55

A= 7/2*( 2/5*7 + 2/7*9  +  ... + 2/53*55 )

A= 7/2*( 7-5/5*7 + 9-7/7*9 + ... + 55-53/53*55 )

A= 7/2*( 1/5-1/7 + 1/7-1/9 + ... + 1/53-1/55 )

A= 7/2*( 1/5-1/55 )

A= 7/2*2/11

A= 7/11

A= 7/11 > 1/2

 Nên: A > 1/2

 

B= 1/3 + 1/15 + 1/35 + ... + 1/99

B= 1/1*3 + 1/3*5 + 1/5*7 + ... + 1/9*11

B= 2*( 2/1*3 + 2/3*5 + 1/5*7 + ... + 2/9*11 )

B= 2*( 3-1/1*3 + 5-3/3*5 + 7-5/5*7 + ... + 11-9/9*11 )

B= 2*( 1/1-1/3 + 1/3-1/5 + 1/5-1/7 + ... + 1/9-1/11 )

B= 2*( 1/1-1/11 )

B= 2*10/11

B= 20/11

B= 20/11 < 1/2

Nên: B < 1/2

\(A=\dfrac{1}{5\times7}+\dfrac{1}{7\times9}+\dfrac{1}{9\times11}+...+\dfrac{1}{87\times89}\)

\(A=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{87}-\dfrac{1}{89}\)

\(A=\dfrac{1}{5}-\left(\dfrac{1}{7}-\dfrac{1}{7}\right)-\left(\dfrac{1}{9}-\dfrac{1}{9}\right)-...-\left(\dfrac{1}{87}-\dfrac{1}{87}\right)-\dfrac{1}{89}\)

\(A=\dfrac{1}{5}-\dfrac{1}{89}\)

\(A=\dfrac{84}{445}\)

Vậy, `A=84/445.`

6 tháng 6 2023

A = \(\dfrac{1}{5\times7}\) + \(\dfrac{1}{7\times9}\)+\(\dfrac{1}{9\times11}\)+...+\(\dfrac{1}{87\times89}\)

A = \(\dfrac{1}{2}\) \(\times\)(  \(\dfrac{2}{5\times7}\)+\(\dfrac{2}{7\times9}\)+\(\dfrac{2}{9\times11}\)+...+\(\dfrac{2}{87\times89}\))

A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{11}\) +...+ \(\dfrac{1}{87}\) - \(\dfrac{1}{89}\))

A = \(\dfrac{1}{2}\) \(\times\) (\(\dfrac{1}{5}\) - \(\dfrac{1}{89}\))

A = \(\dfrac{1}{2}\) \(\times\) \(\dfrac{84}{445}\) 

A = \(\dfrac{42}{445}\)

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}.\left(\frac{1}{8.9}-\frac{1}{9.10}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)

\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{9.10}\right)=\frac{1}{2}.\frac{22}{45}=\frac{11}{45}\)

27 tháng 7 2015

\(\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\right)\times y=\frac{2}{3}\)

\(\frac{1}{2}\times\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\times y=\frac{2}{3}\)

\(\frac{1}{2}\times\left(\frac{1}{1}-\frac{1}{11}\right)\times y=\frac{2}{3}\)

\(\frac{1}{2}\times\frac{10}{11}\times y=\frac{2}{3}\)

\(\frac{5}{11}\times y=\frac{2}{3}\) => \(y=\frac{2}{3}:\frac{5}{11}=\frac{2}{3}\times\frac{11}{5}=\frac{22}{15}\)

2 tháng 8 2016

\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\)

\(=\frac{1}{1}-\frac{1}{11}=\frac{10}{11}\)

5 tháng 11 2016

A.  = 1/2-1/3+1/3-1/4+1/4-1/5...+1/101-1/102=1/2-1/102=25/51.

B.  =1/5-1/10+1/10-1/15+...+1/115-1/120=1/5-1/120=23/120.

C.  = 1/5-1/7+1/7-1/9+1/9-1/11+...+1/997-1/999=1/5-1/999=994/4995.

Minh kiem tra bang may tinh roi do.

5 tháng 11 2016

\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{101\times102}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{101}-\frac{1}{102}+\frac{1}{102}\)

\(=1-\frac{1}{102}\)

\(=\frac{101}{102}\)

12 tháng 1 2016

tich mik mik tich lai cho

12 tháng 1 2016

các bạn giải hẳn cho mình đi

19 tháng 7 2018

\(a,\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\)

\(=\frac{13}{15}+\frac{13}{35}+\frac{13}{63}+\frac{13}{99}\)

\(=13\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{7.9}\right)\)

\(=13\left(\frac{1}{3}-\frac{1}{9}\right)\)

\(=13.\frac{2}{9}=\frac{26}{9}\)

\(b,\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)

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

\(=1-\frac{1}{2018}=\frac{2017}{2018}\)

P/s :Dấu chấm là dấu nhân nha

19 tháng 7 2018

phần c đâu bn