Ta có: \(\dfrac{1}{1\cdot5}+\dfrac{1}{5\cdot10}+...+\dfrac{1}{2010\cdot2015}\)

\(=\dfrac{1}{5}+\dfrac{1}{5}\left(\dfrac{5}{5\cdot10}+\dfrac{5}{10\cdot15}+...+\dfrac{5}{2010\cdot2015}\right)\)

\(=\dfrac{1}{5}+\dfrac{1}{5}\left(\dfrac{1}{5}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{15}+...+\dfrac{1}{2010}-\dfrac{1}{2015}\right)\)

\(=\dfrac{1}{5}+\dfrac{1}{5}\left(\dfrac{1}{5}-\dfrac{1}{2015}\right)\)

\(=\dfrac{1}{5}+\dfrac{1}{5}\cdot\dfrac{402}{2015}\)

\(=\dfrac{1}{5}\left(1+\dfrac{402}{2015}\right)\)

\(=\dfrac{1}{5}\cdot\dfrac{2417}{2015}=\dfrac{2417}{10075}\)

(5/5x10+5/10x15+5/15x20+...+5/95x100)

=  (1/5-1/10+1/10-1/15+1/15-1/20+....+1/95-1/100):5

=(1/5-1/100):5

=19/500

N = 1/1x5 + 1/5x10 + 1/10x15 + 1/15x20 + .....+1/2005 x 2010

N = 1 - 1/5 +1/5-1/5+1/10-1/15+1/5-1/20+.....+1/2005-1/2010

N = 1 - 1/2010

N = 2009/2010

Ta có:

\(N=\frac{1}{1x5}+\frac{1}{5x10}+\frac{1}{10x15}...+\frac{1}{2005x2010}\)

\(\Rightarrow Nx5=\left(\frac{1}{1x5}+\frac{1}{5x10}+\frac{1}{10x15}...+\frac{1}{2005x2010}\right)x5\)

\(=\frac{5}{1x5}+\frac{5}{5x10}+\frac{5}{10x15}...+\frac{5}{2005x2010}\)

\(=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{2005}-\frac{1}{2010}\)

\(=1-\frac{1}{2010}\)

\(=\frac{2009}{2010}\)

\(\Rightarrow N=\frac{2009}{2010}:5=\frac{2009}{2010}x\frac{1}{5}=\frac{2009}{10050}\)

Bạn thuỳ dung ơi cho hỏi sao 5/(1x5) = 1 - 1/5 vậy ???

`2/5 xx 10/21 xx 52`

`= ( 2xx10xx52)/(5xx21)`

`=1040/105`

`=208/21`

`----`

`(1/2 + 3/4) xx 4`

`=(2/4 + 3/4) xx4`

`= 5/4 xx 4`

`=20/4`

`=5`

A = \(\dfrac{1}{1\times2}\) + \(\dfrac{3}{2\times5}\) + \(\dfrac{5}{5\times10}\) + \(\dfrac{4}{10\times14}\) + \(\dfrac{6}{14\times20}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{10}\) + \(\dfrac{1}{10}\) - \(\dfrac{1}{14}\) + \(\dfrac{1}{14}\) - \(\dfrac{1}{20}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{20}\)

A = \(\dfrac{19}{20}\)

\(\frac{2x3x5}{70}\)= \(\frac{2x3x5}{2x5x7}\)= \(\frac{3}{7}\)

Đây là cách làm của bài này

Chúc bạn học tốt!

\(\frac{2x3x5}{70}=\frac{2x3x5}{2x5x7}=\frac{3}{7}\)

Các bạn ủng hộ mk nha

2x3x5/70 = 2x3x5/2x5x7 = 3/7

1 - 1 + 9 x 9 = 81 nha

1-1+9x9

=0+81

=81

bằng 81 nha bạn

Câu trả lời của mình :

1-1+9x9=81 (nha)

A = 1/5×10 + 1/10×15 + ... + 1/100×105

A = 1/5×5 × (1/1×2 + 1/2×3 + ... + 1/20×21)

A = 1/25 × (1 - 1/2 + 1/2 - 1/3 + ... + 1/20 - 1/21)

A = 1/25 × (1 - 1/21)

A = 1/25 × 20/21

A = 4/105

A = \(\frac{1}{5.10}+\frac{1}{10.15}+...+\frac{1}{100.105}\)

A = \(\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...\frac{1}{100}-\frac{1}{105}\)

A = \(\frac{1}{5}-\frac{1}{105}\)

A = \(\frac{20}{105}\)

K MK NHA

\(A=\frac{1}{5.10}+\frac{1}{10.15}+....+\frac{1}{100.105}=\frac{1}{5}\left(\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+....+\frac{1}{100}-\frac{1}{105}\right)\)

\(\Rightarrow A=\frac{1}{5}\left(\frac{1}{5}-\frac{1}{105}\right)=\frac{1}{5}.\frac{4}{21}=\frac{4}{105}\)

(Dấu chấm . là dấu nhân nha bạn)

Xin lỗi mình nhầm:

5 × 10 + 5 × 10 + 90 = 5 × 10 + 5 × 10 + 5 × 18 = 5 × (10 + 10 + 18) = 5 × 38 = 190.

5x10+5x10+900

=50+50+90

=100+90

=190

k mình nha

5 x 10 + 5 x 10 + 90

= 50 + 50 + 90

= 1000 + 90

= 1090

nha Nguyễn Thị Nhàn  please