\(B=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}\)

Ta có : \(\frac{1}{2^2}=\frac{1}{2\cdot2}< \frac{1}{1\cdot2}\)

\(\frac{1}{3^2}=\frac{1}{3\cdot3}< \frac{1}{2\cdot3}\)

...

\(\frac{1}{8^2}=\frac{1}{8\cdot8}< \frac{1}{7\cdot8}\)

Cộng vế theo vế 

\(\Rightarrow B=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{8^2}< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{7\cdot8}\)

\(\Rightarrow B< \frac{1}{1}-\frac{1}{8}=\frac{7}{8}\)

Lại có \(\frac{7}{8}< 1\)

Theo tính chất bắc cầu => \(B< \frac{7}{8}< 1\)

\(\Rightarrow B< 1\left(đpcm\right)\)

a/\(\frac{13}{11}.\frac{22}{26}-x^2=\frac{7}{16}\)

\(\Rightarrow1-x^2=\frac{7}{16}\)

\(\Rightarrow x^2=\frac{9}{16}\)

\(\Rightarrow x=\orbr{\begin{cases}\frac{3}{4}\\-\frac{3}{4}\end{cases}}\)

\(a,\frac{13}{11}.\frac{22}{26}-x^2=\frac{7}{16}\)

\(1-x^2=\frac{7}{16}\)

\(x^2=1-\frac{7}{16}=\frac{9}{16}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{3}{4}\\x=-\frac{3}{4}\end{cases}}\)

\(b,x^2+-\frac{9}{25}=\frac{2}{5}.\frac{8}{5}\)

\(x^2+-\frac{9}{25}=\frac{16}{25}\)

\(x^2=\frac{16}{25}--\frac{9}{25}=1\)

\(\Rightarrow\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)

học tốt ~~~

a/ \(\frac{13}{11}.\frac{22}{26}-x^2=\frac{7}{16}\)

\(\Rightarrow\)\(1-x^2=\frac{7}{16}\)

\(\Rightarrow\)\(x^2=1-\frac{7}{16}\)

\(\Rightarrow\)\(x^2=\frac{9}{16}\)

\(\Rightarrow\)\(x^2=\left(\frac{3}{4}\right)^2\)

\(\Rightarrow\)\(x=\frac{3}{4}\)

b, \(x^2+\frac{-9}{25}=\frac{2}{5}.\frac{8}{5}\)

\(\Rightarrow x^2+\frac{-9}{25}=\frac{16}{25}\)

\(\Rightarrow x^2=\frac{16}{25}-\frac{-9}{25}\)

\(\Rightarrow x^2=\frac{25}{25}\)

\(\Rightarrow x^2=\left(\frac{5}{5}\right)^2=\left(\frac{-5}{5}\right)^2\)

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

\(\Rightarrow x=1=-1\)

\(\Rightarrow x=\pm1\)

làm cho 1 cái những cái sau tương tự mà lm nha bạn

\(\frac{x}{5}=-\frac{6}{7}\)

\(=>7x=-6\cdot5\)

\(7x=-30\)

\(x=-\frac{30}{7}\)

\(\frac{x}{2}=-\frac{8}{-x}\)

\(=>\frac{x}{2}=\frac{8}{x}\)

\(=>xx=8\cdot2\)

\(x^2=16\)

\(=>x\in\left\{-4;4\right\}\)

\(\frac{1+0,6-\frac{3}{7}}{\frac{8}{3}+\frac{8}{5}-\frac{8}{7}}=\frac{\frac{3}{3}+\frac{3}{5}-\frac{3}{7}}{\frac{8}{3}+\frac{8}{5}-\frac{8}{7}}=\frac{3.\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{7}\right)}{8.\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{7}\right)}=\frac{3.1}{8.1}=\frac{3}{8}\)

\(\frac{\frac{1}{3}+0,25-\frac{1}{5}+0,125}{\frac{7}{6}+\frac{7}{8}-0,7+\frac{7}{16}}=\frac{\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{8}}{\frac{7}{6}+\frac{7}{8}-\frac{7}{10}+\frac{7}{16}}=\frac{1.\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{8}\right)}{7.\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{8}\right)}=\frac{1.1}{7.1}=\frac{1}{7}\)

=>\(\frac{3}{8}-\frac{1}{7}=\frac{13}{56}\)

Mk đg cần gấp các bn giúp mk nha

Cảm ơn bạn nha,  Nguyễn Thành An

a) BPT <=> \(\left(\frac{x+2}{98}+1\right)+\left(\frac{x+3}{97}+1\right)>\left(\frac{x+4}{96}+1\right)+\left(\frac{x+5}{95}+1\right)\)

<=> \(\frac{x+100}{98}+\frac{x+100}{97}>\frac{x+100}{96}+\frac{x+100}{95}\)

<=> \(\left(x+100\right)\left(\frac{1}{98}+\frac{1}{97}-\frac{1}{96}-\frac{1}{95}\right)>0\)

Mà \(\frac{1}{98}+\frac{1}{97}-\frac{1}{96}-\frac{1}{95}< 0\)

<=> x + 100 < 0

<=> x < -100

b) BPT <=> \(\left(\frac{x-10}{5}-1\right)+\left(\frac{x-9}{6}-1\right)< \left(\frac{x-8}{7}-1\right)+\left(\frac{x-7}{8}-1\right)\)

<=> \(\frac{x-15}{5}+\frac{x-15}{6}< \frac{x-15}{7}+\frac{x-15}{8}\)

<=> \(\left(x-15\right)\left(\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}\right)< 0\)

Mà \(\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}>0\)

<=> x - 15 < 0

<=> x < 15

a) \(4+x=\frac{x+1}{5}\)

\(5.\left(4+x\right)=x+1\)

\(20+5.x=x+1\)

\(5.x-x=1-20\)

4.x = -19

x = -19/4

2) \(\frac{7}{x-1}=\frac{x}{8}\)

\(x.\left(x-1\right)=7.8\) ( x; x- 1 là 2 số tự nhiên liên tiếp)

=> x = 8

\(\frac{3x-7}{5}=\frac{2x-1}{3}\)

\(\Leftrightarrow9x-21=10x-5\)

\(\Leftrightarrow-x=16\Leftrightarrow x=-16\)

\(\frac{4x-7}{12}-x=\frac{3x}{8}\)

\(\Leftrightarrow\frac{4x-7-12x}{12}=\frac{3x}{8}\)

\(\Leftrightarrow\frac{-7-8x}{12}=\frac{3x}{8}\)

\(\Leftrightarrow-56-64x=36x\)

\(\Leftrightarrow-56=100x\Leftrightarrow x=\frac{-14}{25}\)

\(\frac{x-2009}{1234}+\frac{x-2009}{5678}-\frac{x-2009}{197}=0\)

\(\Leftrightarrow\left(x-2019\right)\left(\frac{1}{1234}+\frac{1}{5678}-\frac{1}{197}\right)=0\)

Vì \(\left(\frac{1}{1234}+\frac{1}{5678}-\frac{1}{197}\right)\ne0\)nên x - 2019 = 0

Vậy x = 2019

\(\frac{5x-8}{3}=\frac{1-3x}{2}\)

\(\Leftrightarrow10x-16=3-9x\)

\(\Leftrightarrow19x=19\Leftrightarrow x=1\)

\(\frac{x-5}{6}-\frac{x-9}{4}=\frac{5x-3}{8}+2\)

\(\Rightarrow\frac{4x-20-6x+54}{24}=\frac{5x-3+16}{8}\)

\(\Rightarrow\frac{-2x+34}{24}=\frac{5x+13}{8}\)

\(\Rightarrow-16x-272=120x+312\)

\(\Leftrightarrow-136x=584\Leftrightarrow x=\frac{-73}{17}\)

a)\(\frac{x+3}{x+5}=7\Leftrightarrow x+3=7\left(x+5\right)\)

\(\Leftrightarrow x+3=7x+35\)

\(\Leftrightarrow-6x=32\)

\(\Leftrightarrow x=-\frac{16}{3}\)

b)\(\frac{2x-1}{3x+5}=-\frac{2}{3}\)

\(\Leftrightarrow3\left(2x-1\right)=-2\left(3x+5\right)\)

\(\Leftrightarrow6x-3=-6x-10\)

\(\Leftrightarrow12x=-7\)

\(\Leftrightarrow x=-\frac{7}{12}\)

c)\(\frac{x+1}{4}=\frac{9}{x+1}\Leftrightarrow\left(x+1\right)^2=36\)

\(\Leftrightarrow\left(x+1\right)^2=6^2\)

\(\Leftrightarrow\orbr{\begin{cases}x+1=6\\x+1=-6\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=-7\end{cases}}}\)

d)\(\frac{6x-1}{2x+3}=\frac{3x}{x+2}\)

\(\Leftrightarrow\left(6x-1\right)\left(x+2\right)=3x\left(2x+3\right)\)

\(\Leftrightarrow6x^2+12x-x-2=6x^2+9x\)

\(\Leftrightarrow2x=2\Leftrightarrow x=1\)

e)\(\frac{x+1}{x-3}=\frac{x+5}{x-2}\Leftrightarrow\left(x+1\right)\left(x-2\right)=\left(x-3\right)\left(x+5\right)\)

\(\Leftrightarrow x^2-2x+x-2=x^2+5x-3x-15\)

\(\Leftrightarrow-3x=-13\)

\(\Leftrightarrow x=\frac{13}{3}\)

f)\(\frac{x+4}{x+5}=\frac{x+6}{x+7}\Leftrightarrow\left(x+4\right)\left(x+7\right)=\left(x+5\right)\left(x+6\right)\)

\(\Leftrightarrow x^2+11x+28=x^2+11x+30\)

\(\Leftrightarrow0x=2\)

\(\Leftrightarrow x\in\varnothing\)