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3 tháng 3 2016

Gọi dãy trên là A

3/5A=3(4.7)+3/(7.10)+......+(3/(31+34)

=1/4-1/7+1/7-1/10+........+1/31-1/34

=1/4-1/34=15/68

12 tháng 8 2016

A=3/4.7+3/7.10+.........+3/31,34

29 tháng 6 2017

Đặt : \(A=\frac{5}{1\cdot4}+\frac{5}{4\cdot7}+\frac{5}{7\cdot10}+...+\frac{5}{27\cdot30}\)

\(A=\frac{1}{3}\left(\frac{5}{1}-\frac{5}{4}+\frac{5}{4}-\frac{5}{7}+...+\frac{5}{27}-\frac{5}{30}\right)\)

\(A=\frac{1}{3}\left(5-\frac{5}{30}\right)\)

\(A=\frac{1}{3}\cdot\frac{29}{6}\)

\(A=\frac{29}{18}\)

29 tháng 6 2017

\(\frac{5}{1.4}+\frac{5}{4.7}+\frac{5}{7.10}+....+\frac{5}{27.30}\)

\(=\frac{4-1}{1.4}+\frac{7-4}{4.7}+\frac{10-7}{7.10}+...+\frac{30-27}{27.30}\)

\(=\frac{5}{3}\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+....+\frac{1}{27}-\frac{1}{30}\right)\)

\(=\frac{5}{3}\cdot\left(1-\frac{1}{30}\right)\)

\(=\frac{5}{3}\cdot\frac{29}{30}=\frac{29}{18}\)

4 tháng 8 2016

A=\(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{73.76}\)

3A=3(\(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{73.76}\))

3A=\(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{73.76}\)

3A=\(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{73}+\frac{1}{76}\)

3A=\(\frac{1}{4}-\frac{1}{76}\)

3A=\(\frac{9}{38}\)

A=\(\frac{9}{38}\):3

A=\(\frac{3}{38}\)

4 tháng 8 2016

đặt A=1/4.7+1/7.10+...+1/73.76

3A=1/4-1/7+1/7-1/10+...+1/ 73 -1/ 76
 

2 tháng 8 2018

các bn trả lời nhanh nhé

đến 9:10 nhé

2 tháng 8 2018

\(A=\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+.....+\frac{2}{73.76}\)

\(=\frac{2}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+....+\frac{3}{73.76}\right)\)

\(=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+....+\frac{1}{73}-\frac{1}{76}\right)\)

\(=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{76}\right)\)

\(=\frac{2}{3}.\frac{9}{38}=\frac{3}{19}\)

5 tháng 4 2016

4/1.4+4/4.7+4/7.10+4/10.13

= 4/3(3/1.4+3/4.7+3/7.10+3/10.13)

=4/3(1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13)

=4/3(1/1-1/13)

=4/3.12/13

=16/13

6 tháng 4 2017

\(\frac{5}{1.4}+\frac{5}{4.7}+\frac{5}{7.10}+...+\frac{5}{100.103}\)

\(=\frac{5}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{100}-\frac{1}{103}\right)\)

\(=\frac{5}{3}\left(1-\frac{1}{103}\right)\)

\(=\frac{5}{3}.\frac{102}{103}=\frac{170}{103}\)

6 tháng 4 2017

\(\frac{5}{1.4}+\frac{5}{4.7}+\frac{5}{7.10}+...+\frac{5}{100.103}=\frac{5}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{100.103}\right)=\frac{5}{3}.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{100}-\frac{1}{103}\right)=\frac{5}{3}.\left(\frac{1}{1}-\frac{1}{103}\right)=\frac{5}{3}.\frac{102}{103}=\frac{170}{103}\)

12 tháng 8 2015

B = \(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{301.304}\)

B = \(\frac{1}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{301}-\frac{1}{304}\right)\)

B = \(\frac{1}{3}.\left(\frac{1}{4}-\frac{1}{304}\right)\)

B = \(\frac{1}{3}.\frac{75}{304}\)

B = \(\frac{25}{304}\)

12 tháng 8 2015

\(B=\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{301.304}\right):3\)

\(\Rightarrow B=\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{301}-\frac{1}{304}\right):3\)

\(\Rightarrow B=\left(\frac{1}{4}-\frac{1}{304}\right):3\)

\(\Rightarrow B=\frac{75}{304}:3=\frac{25}{304}\)

17 tháng 5 2019

\(\frac{3x}{4.7}+\frac{3x}{7.10}+\frac{3x}{10.13}+\frac{3x}{13.16}+...+\frac{3x}{19.22}=\frac{-5}{88}\)

\(\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+...+\frac{3}{19.22}\right)x=\frac{-5}{88}\)

\(\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+...+\frac{1}{19}-\frac{1}{22}\right)x=\frac{-5}{88}\)

\(\left[\frac{1}{4}+\left(\frac{1}{7}-\frac{1}{7}\right)+\left(\frac{1}{10}-\frac{1}{10}\right)+...+\left(\frac{1}{19}-\frac{1}{19}\right)-\frac{1}{22}\right]x=\frac{-5}{88}\)

\(\left[\frac{1}{4}-\frac{1}{22}\right]x=\frac{-5}{88}\)

\(\frac{9}{44}x=\frac{-5}{88}\)

\(x=\frac{-5}{88}:\frac{9}{44}\)

\(x=\frac{-5}{18}\)

~ Hok tốt ~

17 tháng 5 2019

#)Giải :

Đặt \(A=\frac{3x}{2.7}+\frac{3x}{7.10}+\frac{3x}{10.13}+\frac{3x}{13.16}+...+\frac{3x}{19.22}=-\frac{5}{88}\)

\(A=\frac{3x}{2}+\frac{3x}{7}-\frac{3x}{7}+\frac{3x}{10}-\frac{3x}{10}+\frac{3x}{13}-\frac{3x}{13}+\frac{3x}{16}-...-\frac{3x}{19}+\frac{3x}{22}=-\frac{5}{88}\)

\(A=\frac{3x}{2}+0+0+0+...+0+\frac{3x}{22}=-\frac{5}{88}\)

\(A=\frac{3x}{2}+\frac{3x}{22}=-\frac{5}{88}\)

\(3x:\left(2+22\right)=-\frac{5}{88}\)

\(3x:24=-\frac{5}{88}\)

\(3x=-\frac{5}{88}.24\)

\(3x=-\frac{7}{11}\)

\(x=-\frac{7}{11}:3\)

\(x=-\frac{7}{33}\)

              #~Will~be~Pens~#

27 tháng 4 2016

Ta thấy: 1/1-1/4 = 3/4 = 3.(1/1.4)

           1/4-1/7 = 3/28 = 3.(1/4.7)

A = 3(1/1-1/4+1/4-1/7+...+1/97-1/100)

A = 3.(1-1/100)

A = 3.(99/100)

A = 297/100

27 tháng 4 2016

\(A=\frac{1}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.......+\frac{1}{97}-\frac{1}{100}\right)\)

\(A=\frac{1}{3}.\left(1-\frac{1}{100}\right)\)

\(A=\frac{1}{3}.\frac{99}{100}\)

\(A=\frac{33}{100}\)

28 tháng 3 2017

a,1/1-1/4+1/4-1/7+...+1/2008-1/2011

=(1-1/2011)+(-1/4+1/4)+...+(-1/2008+1/2008)

=1-1/2011+0+...+0

=1-1/2011

=2010/2011