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5 tháng 4 2015

\(5A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{\left(5n+1\right).\left(5n+6\right)}\)

\(5A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{5n+1}-\frac{1}{5n+6}\)

\(5A=1-\frac{1}{5n+6}=\frac{5n+6-1}{5n+6}=\frac{5n+5}{5n+6}\)=> \(A=\frac{n+1}{5n+6}\)

\(A=\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+...+\frac{1}{\left(5n+1\right)\cdot\left(5n+6\right)}\)\(5A=\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+...+\frac{5}{\left(5n+1\right)\cdot\left(5n+6\right)}\)\(5A=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{5n+1}-\frac{1}{5n+6}\)

3 tháng 4 2016

1/1x2x3+1/2x3x4+...1/118x19x20<1/4 <--- cái này đề sai ở 1/118x19x20 phải là 1/18x19x20

12 tháng 3 2015

mình trả lời bài 1 thôi nhé :

Gọi biểu thức trên là A.

Theo bài ra ta có:A=1/1.6+1/6.11+1/11.16+...+1/(5n+1)+1/(5n+6)

                           =1/5(1-1/6+1/6-1/11+1/11-1/16+...+1/5n+1-1/5n+6)

                           =1/5(1-1/5n+6)

                           =1/5( 5n+6/5n+6-1/5n+6)

                           =1/5(5n+6-1/5n+6)

                           =1/5.5n+5/5n+6

                           =n+1/5n+6

                           =ĐIỀU PHẢI CHỨNG MINH

 

30 tháng 4 2015

x- 20/11.13 - 20/13.15 - 20/13.15 - 20/15.17 -...- 20/53.55=3/11

x-10.(2/11.13+2/13.15+2/15.17+...+2/53.55=3/11

x-10.(1/11-1/13+1/13-1/15+1/15-1/17+...+1/53-1/55)=3/11

x-10.(1/11-1/55)=3/11

x-10.4/55=3/11

x-8/11=3/11

x = 3/11+8/11

x=11/11=1

****

9 tháng 8 2019

Ta có : \(A=\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}+...+\frac{1}{(5n+1)(5n+6)}\)

\(=\frac{1}{5}\cdot\left[\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{5}{(5n+1)(5n+6)}\right]\)

\(=\frac{1}{5}\cdot\left[1-\frac{1}{5n+6}\right]=\frac{1}{5}\cdot\frac{5n+6-1}{5n+6}=\frac{1}{5}\cdot\frac{5(n+1)}{5n+6}=\frac{n+1}{5n+6}\)

23 tháng 7 2017
14 101.16 101=(14.16)mũ 101=224 mũ 101=(224 mũ 2)mũ 50.224=(..76) mũ50.224=(..76).224=(...24)
8 tháng 8 2023

 CM:  \(\dfrac{1}{1.6}\)\(\dfrac{1}{11.16}\)+...+ \(\dfrac{1}{\left(5n+1\right)\left(5n+6\right)}\) = \(\dfrac{n+1}{5n+6}\)

A = \(\dfrac{1}{5}\)(\(\dfrac{5}{1.6}\) + \(\dfrac{5}{6.11}\)+...+ \(\dfrac{5}{\left(5n+1\right).\left(5n+6\right)}\)

A = \(\dfrac{1}{5}\).( \(\dfrac{1}{1}\) - \(\dfrac{1}{6}\)\(\dfrac{1}{6}\) - \(\dfrac{1}{11}\)+...+ \(\dfrac{1}{5n+1}\) - \(\dfrac{1}{5n+6}\))

A = \(\dfrac{1}{5}\) .( \(\dfrac{1}{1}\) - \(\dfrac{1}{5n+6}\))

A = \(\dfrac{1}{5}\)\(\dfrac{5n+6-1}{5n+6}\)

A = \(\dfrac{1}{5}\)\(\dfrac{5n+5}{5n+6}\)

A = \(\dfrac{1}{5}\) . \(\dfrac{5.\left(n+1\right)}{5n+6}\)

A = \(\dfrac{n+1}{5n+6}\)

\(\dfrac{1}{1.6}\) + \(\dfrac{1}{6.11}\)\(\dfrac{1}{11.16}\)+...+ \(\dfrac{1}{\left(5n+1\right)\left(5n+6\right)}\) = \(\dfrac{n+1}{5n+1}\) (đpcm)

 

 

8 tháng 8 2023

\(A=\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+...+\dfrac{1}{\left(5n+1\right)\left(5n+6\right)}\)

\(A=\dfrac{1}{5}\left[1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{5n+1}-\dfrac{1}{5n+6}\right]\)

\(A=\dfrac{1}{5}\left(1-\dfrac{1}{5n+6}\right)\)

\(A=\dfrac{1}{5}\left(\dfrac{5n+6-1}{5n+6}\right)=\dfrac{1}{5}\left(\dfrac{5n+5}{5n+6}\right)=\dfrac{1}{5}.5\left(\dfrac{n+1}{5n+6}\right)=\dfrac{n+1}{5n+6}\)

\(\Rightarrow dpcm\)

29 tháng 4 2016

Gọi A = 1/1.6 + 1/6.11 +...+ 1/(5n+1)(5n+6) 

5A = 5/1.6 + 5/6.11 + ... + 5/(5n+1)(5n+6)

     =1 - 1/6 + 1/6 - 1/11 + ... + 1/5n+1 - 1/5n+6 

    =1 - 1/5n+6 =5n+6/5n+6 - 1/5n+6=5n+5 /5n+6

29 tháng 4 2016

tôi không hiểu???

28 tháng 3