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15 tháng 9 2023

a. \(\dfrac{1}{2.4}\) + \(\dfrac{1}{4.6}\) + \(\dfrac{1}{6.8}\) + ...... + \(\dfrac{1}{20.22}\)

= 1/2 ( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ..... + 1/20 - 1/22)

=1/2 ( 1/2 - 1/22)

= 1/2 . 5/11

= 5/22

b. 1+ 2/3 + 2/6 + 2/10 +...+ 2/45

=>1/2.(1+2/3+2/6+....+2/45)=1/2+2/6+2/12+...+2/90

=1/2+2/2.3+2/3.4+...+2/9.10
=2.(1/4+3-2/2.3+4-3/3.4+...+10-9/9.10)

=2. ( 1/4+1/2-1/3+1/3-1/4+.....+1/9-1/10)
= 2.( 1/4-1/10)=2.3/20=3/10

=> vì 1/2.*=3/10

=> *=3/10:1/2=3/5

tick mình nhé

 

16 tháng 9 2023

B = 1 + \(\dfrac{2}{3}\) + \(\dfrac{2}{6}\) +\(\dfrac{2}{10}\) + \(\dfrac{2}{15}\)+...+ \(\dfrac{2}{45}\)

B = 1 + 2.(\(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\)+...+ \(\dfrac{1}{45}\))

B = 1 + \(\dfrac{4}{2}\).(\(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) +\(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) + ...+ \(\dfrac{1}{45}\))

B = 1 + 4.( \(\dfrac{1}{6}\) +\(\dfrac{1}{12}\)\(\dfrac{1}{20}\)\(\dfrac{1}{30}\)+...+ \(\dfrac{1}{90}\))

B = 1 + 4.(\(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\)\(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\)+...+\(\dfrac{1}{9.10}\))

B = 1 + 4 .( \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\)+...+ \(\dfrac{1}{9}\) - \(\dfrac{1}{10}\))

B = 1 + 4.( \(\dfrac{1}{2}\) - \(\dfrac{1}{10}\))

B = 1 + 4. \(\dfrac{2}{5}\)

B = \(\dfrac{13}{5}\)

 

Câu 3:

UCLN(48;60)=12

UC(48;60)={1;2;3;4;6;12}

Câu 4: 

Gọi số học sinh là x

Theo đề, ta có: \(x\in BC\left(3;4;6\right)\)

hay x=48

5 tháng 1 2022

\(a,x-15=20.2^2\)

\(\Leftrightarrow x-15=80\)

\(\Leftrightarrow x=95\)

\(b,48+5\left(x-3\right)=63\)

\(\Leftrightarrow5\left(x-3\right)=15\)

\(\Leftrightarrow x-3=3\)

\(\Leftrightarrow x=6\)

còn lại ad Nguyễn Lê Phước Thịnh làm r nha

17 tháng 4 2017

A=\(\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+\dfrac{1}{6\cdot8}+...+\dfrac{1}{20\cdot22}\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{20}-\dfrac{1}{22}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{22}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{11}{22}-\dfrac{1}{22}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{5}{11}\)

\(=\dfrac{5}{22}\)

17 tháng 4 2017

Mk có thể làm wen đc k

leuleu

12 tháng 9 2018

\(6B=2.4.6+4.6.6+6.8.6+8.10.6+...+20.22.6.\)

\(6B=2.4.6+4.6.\left(8-2\right)+6.8.\left(10-4\right)+8.10.\left(12-6\right)+...+20.22.\left(24-18\right)\)

\(6B=2.4.6-2.4.6+4.6.8-4.6.8+6.8.10-6.8.10+8.10.12-...-18.20.22+20.22.24\)

\(6B=20.22.24\Rightarrow B=\frac{20.22.24}{6}=4.20.22=1760\)

12 tháng 9 2018

Cảm ơn cậu nhé!!!!!! 

9 tháng 2 2018

\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{20.22}\right)\)

\(=\frac{1.3+1}{1.3}.\frac{2.4+1}{2.4}.\frac{3.5+1}{3.5}.....\frac{20.22+1}{20.22}\)

\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{21^2}{20.22}\)

\(=\frac{\left(2.3.4.....21\right)\left(2.3.4.....21\right)}{\left(1.2.3.....20\right)\left(3.4.5.....22\right)}\)

\(=\frac{21.2}{22}=\frac{42}{22}=\frac{21}{11}\)

15 tháng 4 2019

ĐỪNG ẤN ĐỌC THÊM

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Đã kêu đừng ấn mà đéo nghe :))))

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Lần này nữa thôi :)))

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15 tháng 4 2019

B = \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{18.19.20}\)

=>  2B =   \(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{18.19.20}\)

2B  = \(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{18.19}-\frac{1}{19.20}\)

2B =   \(\frac{1}{1.2}-\frac{1}{19.20}\)

2B =  \(\frac{189}{380}\)

B = \(\frac{189}{380}:2\)

B = \(\frac{189}{760}\). Nhớ tích nhoa !!

23 tháng 3 2017

\(B=\frac{3}{4.6}+\frac{3}{6.8}+\frac{3}{8.10}+...+\frac{3}{20.22}\)

\(=\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+...+\frac{1}{20.22}\)

\(=\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{20}-\frac{1}{22}\right)\)

\(=\frac{1}{4}-\frac{1}{22}\)

\(=\frac{9}{44}\)

23 tháng 3 2017

A = 1111 x ( 1/2 - 1/3 - 1/6 )

A = 1111 x 0 = 0

B = 3/4 x 6 + 3/6 x 8 + 3/8 x 10 + ... + 3/20 x 22

B = 3/2 ( 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/20 - 1/22 )

B = 3/2 x ( 1/4 - 1/22 )

B = 3/2 x 9/44 = 27/88