Theo đề suy ra

\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{3}{10}\)

=> \(\frac{1}{3}-\frac{1}{x+1}=\frac{3}{10}\)

\(\frac{1}{x+1}=\frac{1}{3}-\frac{3}{10}=\frac{1}{30}\)

=>x+1=30

=>x=29

Quá dễ:

=> 1/3 - 1/4 + 1/4 - 1/5 + ....+ 1/x - 1/x+1 = 3/10

=> 1/3 - 1/x+1 = 3/10

=> 1/x+1 = 1/3 - 3/10

Còn lại tự làm nhá!

<=> 1/3 - 1/(x+1) = 3/10 

<=> 1/(x+1) = 1/30

=> x+1 = 30 

<=> x= 29 

= > 1/3 - 1/4 +1/4 -1/5 + ..... + 1/x - 1/x+1 = 3/10

= > 1/3 - 1/x+1 = 3/10

= > 1/x+1         = 1/3 - 3/10

= > 1/x+1         =1/30 

= > x+1 = 30

= > x     = 29

Vậy x = 29

\(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{x\left(x+1\right)}=\frac{3}{10}\)

\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{3}{10}\)

\(\frac{1}{3}-\frac{1}{x+1}=\frac{3}{10}\)

\(\frac{1}{x+1}=\frac{1}{30}\)

\(x+1=30\)

\(x=29\)

\(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+....+\frac{1}{x\left(x+1\right)}=\frac{3}{10}\left(x\ne0;x\ne-1\right)\)

\(\Leftrightarrow\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{3}{10}\)

\(\Leftrightarrow\frac{1}{3}-\frac{1}{x+1}=\frac{3}{10}\)

\(\Leftrightarrow\frac{x+1}{3\left(x+1\right)}-\frac{3}{3\left(x+1\right)}=\frac{3}{10}\)

\(\Leftrightarrow\frac{x-2}{3\left(x+1\right)}=\frac{3}{10}\)

<=> 10(x-2)=3.3(x+1)

<=> 10x-20=9(x+1)

<=> 10x-20=9x+1

<=> 10x-20-9x-1=0

<=> x-21=0

<=> x=21 (tmđk)

Vậy x=21

\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)x<\frac{13}{7}\)

\(\left(1-\frac{1}{7}\right).x<\frac{13}{7}\)

\(\frac{6}{7}.x<\frac{13}{7}\Leftrightarrow6x<13\Leftrightarrow x<2,1\left(6\right)\)

x nguyên dương => x thuộc {1;2}

Vậy tập hợp có 2 phần tử

vay tap hop co 2 phan tu

vì vế trái dương nên vế phải dương nên x dương

chúng ta có thể phá  dấu GTTĐ

\(\Leftrightarrow2014x+\left(\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{2016}-\frac{1}{2017}\right)=2015x\)

\(\Leftrightarrow x=\frac{1}{3}-\frac{1}{2017}=\frac{2014}{6051}\)

đúng 100%

\(2014.x+\left(\frac{1}{3}-\frac{1}{2017}\right)=2015x\Rightarrow x=\frac{2014}{3.2017}=\frac{2014}{3.2017}\)

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=\frac{1}{2}-\frac{1}{7}\)

\(=\frac{7}{14}-\frac{2}{14}\)

\(=\frac{5}{14}\)

#)Giải :

Gọi các tổng trên là A

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(\Rightarrow A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(\Rightarrow A=\frac{1}{2}-\frac{1}{6}\)

\(\Rightarrow A=\frac{1}{3}\)

         #~Will~be~Pens~#

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)\(=\frac{1}{2}-\frac{1}{7}=\frac{7}{14}-\frac{2}{14}=\frac{5}{14}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

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

\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{n}-\frac{1}{n+1}\)

\(B=1-\frac{1}{n+1}=\frac{n}{n+1}\)

ui cí này e chưa học

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}=1-\frac{1}{6}\)

\(=\frac{5}{6}\)

\(M=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)

\(M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(M=1-\frac{1}{7}\)

\(M=\frac{6}{7}\)

6/7

k cho mình nha

Kết quả:\(\frac{6}{7}\)

Đúng 100% nhé!!

~Shizadon~