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31 tháng 3 2019

1/3 + 1/15 + 1/35 + ... + 1/143 = 1/1*3 + 1/3*5 + 1/5*7 + ... + 1/11*13 = 1 - 1/3 + 1/3 - 1/5 +... + 1/11 - 1/143 = 1 - 1/143 = 142/143

31 tháng 3 2019

\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{143}\)

\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{11.13}\)

\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{13}\right)\)

\(=\frac{1}{2}.\frac{12}{13}\)

\(=\frac{12}{26}=\frac{6}{13}\)

23 tháng 8 2023

\(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{25}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)

\(=\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+\dfrac{2}{9\cdot11}+\dfrac{2}{11\cdot13}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-...+\dfrac{1}{11}-\dfrac{1}{13}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\left(1-\dfrac{1}{3}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\dfrac{2}{3}\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\dfrac{1}{3}+\dfrac{1}{25}\)

\(=\dfrac{28}{75}\)

24 tháng 8 2023

cám ơi bạn

 

11 tháng 4 2016

A=1/1.3 + 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11 + 1/11.13 + 1/13.15

A=1/1 - 1/3 +1/3 - 1/5 +1/5 -1/7+......+1/13 - 1/15

A=1 - 1/15

A=1/14

11 tháng 4 2016

bạn ơi: 

1/195 mới bằng 1/13.15 mà!!

15 tháng 4 2016

1/15+1/35+1/63+1/99+1/143

=1/3.5+1/5.7+1/7.9+1/9.11+1/11.13

=1/2.(2/3.5+2/5.7+2/7.9+2/9.11+2/11.13

=1/2.(1/3-1/5+1/5-1/7+1/6-1/9+1/9-1/11+1/11-1/13=1/2.(1/3-1/13)=1/2.10/39=5/39

9 tháng 3 2022

tttttttttttttttttttttttttttttttttttttttttttttttttttttttttyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyybanh

16 tháng 3 2016

1/15 + 1/35 + 1/63 + 1/99 + 1/143

đặt A = 1/15 + 1/35 + 1/63 + 1/99 + 1/143

A       = 1/3X5 + 1/5X7 + 1/7X9 + 1/9X11 + 1/11X13

A x 2 = 2 x ( 1/3x5 + 1/5x7 + 1/7x9 + 1/9x11 + 1/11x13 )

A x 2 = 2/3x5 + 2/5x7 + 2/7x9 + 2/9x11 + 2/11x13

A x 2 = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13

A x 2 = 1/3 - 1/13

A x 2 = 13/39 - 3/39

A x 2 = 10/39

A      =10/39 : 2

A       = 5/39

16 tháng 3 2016

1/15 + 1/35 + 1/63 + 1/99 + 1/143   = 5/39 nhé bạn !

26 tháng 2 2022

=\(\dfrac{5}{39}\)

26 tháng 2 2022

Bạn trả lời chi tiết giúp mình

29 tháng 3 2018

Đặt \(A=1\frac{7}{15}-\frac{1}{3}-\frac{1}{15}-\frac{1}{35}-\frac{1}{63}-\frac{1}{99}-\frac{1}{143}-\frac{1}{195}\)

\(\Rightarrow A=\frac{22}{15}-\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\right)\)

Đặt \(B=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)

\(\Rightarrow B=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}+\frac{1}{11\cdot13}+\frac{1}{13\cdot15}\)

\(\Rightarrow2B=2\left(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}+\frac{1}{11\cdot13}+\frac{1}{13\cdot15}\right)\)

\(\Rightarrow2B=\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+\frac{2}{11\cdot13}+\frac{2}{13\cdot15}\)

\(\Rightarrow2B=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)

\(\Rightarrow2B=1-\frac{1}{15}\)

\(\Rightarrow2B=\frac{14}{15}\)

\(\Rightarrow B=\frac{14}{15}:2\Rightarrow B=\frac{7}{15}\)

\(\Rightarrow A=\frac{22}{15}-\frac{7}{15}\Rightarrow A=\frac{15}{15}=1\)

29 tháng 3 2018

đáp án là 59​/15

   mình chắc chắn

                      

25 tháng 6 2023

a=78/35

b=22/12

c=1/1

d=40202090/4040090

e=1,24025667172...

f=871,82

ko biết đúng ko [0_0'] hihi

6 tháng 6 2018

\(\frac{1}{3}+\frac{13}{15}+\frac{33}{35}+\frac{61}{63}+\frac{97}{99}\)\(+\frac{141}{143}\)

\(=\left(1-\frac{2}{3}\right)+\left(1-\frac{2}{15}\right)\)\(+\left(1-\frac{2}{35}\right)+\left(1-\frac{2}{63}\right)\)\(+\left(1-\frac{2}{99}\right)+\left(1-\frac{2}{143}\right)\)

\(=\left(1+1+1+1+1+1\right)-\)\(\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)

\(=6-\)\(\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+\frac{2}{11\times13}\right)\)

\(=6-\)\(\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(=6-\left(1-\frac{1}{13}\right)\)

\(=6-\frac{12}{13}\)

\(=\frac{66}{13}\)