\(4.B=\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{93.97}\) 

            \(4.B=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{93}-\frac{1}{97}\)

            \(4.B=1-\frac{1}{97}\)

             \(4.B=\frac{96}{97}\)

                 \(B=\frac{96}{97}:4\)

                 \(B=\frac{24}{97}\)

a) \(A=3\left|2x-\dfrac{3}{2}\right|+2021^0=3\left|2x-\dfrac{3}{2}\right|+1\ge1\)

\(minA=1\Leftrightarrow2x=\dfrac{3}{2}\Leftrightarrow x=\dfrac{3}{4}\)

b) \(B=2\left|x-6\right|+3\left(2y-1\right)^2+2021^0=2\left|x-6\right|+3\left(2y-1\right)^2+1\ge1\)

\(minB=1\Leftrightarrow\) \(\left\{{}\begin{matrix}x=6\\y=\dfrac{1}{2}\end{matrix}\right.\)

\(A=3\left|2x-\dfrac{3}{2}\right|+1\ge1\\ A_{min}=1\Leftrightarrow2x-\dfrac{3}{2}=0\Leftrightarrow x=\dfrac{3}{4}\\ B=2\left|x-6\right|+3\left(2y-1\right)^2+1\ge1\\ B_{min}=1\Leftrightarrow\left\{{}\begin{matrix}x=6\\y=\dfrac{1}{2}\end{matrix}\right.\)

Sửa đề: \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{x\left(x+2\right)}=\frac{2020}{2021}\) \(Đkxđ:\hept{\begin{cases}x\ne0\\x\ne-2\end{cases}}\)

\(\Rightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{2020}{2021}\)

\(\Leftrightarrow1-\frac{1}{x+2}=\frac{2020}{2021}\)

\(\Leftrightarrow\frac{x+2}{2021}=1\)

\(\Leftrightarrow x=2019\)

Vậy \(x=2019\)

\(\dfrac{2021}{1\cdot5}+\dfrac{2021}{5\cdot9}+...+\dfrac{2021}{x\cdot\left(x+4\right)}=505\)

\(2021\cdot\left(\dfrac{1}{1.5}+\dfrac{1}{5\cdot9}+...+\dfrac{1}{x\cdot\left(x+4\right)}\right)=505\)

\(\dfrac{2021}{4}\cdot\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+...+\dfrac{4}{x\cdot\left(x+4\right)}\right)=505\)

\(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{x}-\dfrac{1}{x+4}=\dfrac{2020}{2021}\)

\(1-\dfrac{1}{x+4}=\dfrac{2020}{2021}\)

\(\dfrac{1}{x+4}=\dfrac{1}{2021}\)

=> \(x+4=2021\)

=> \(x=2017\)

vậy \(x=2017\)

Ta có: \(\dfrac{2021}{1\cdot5}+\dfrac{2021}{5\cdot9}+...+\dfrac{2021}{x\left(x+4\right)}=505\)

\(\Leftrightarrow\dfrac{2021}{4}\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+...+\dfrac{4}{x\left(x+4\right)}\right)=505\)

\(\Leftrightarrow1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{x}-\dfrac{1}{x+4}=\dfrac{2020}{2021}\)

\(\Leftrightarrow-\dfrac{1}{x+4}=\dfrac{2020}{2021}\)

\(\Leftrightarrow x+4=\dfrac{-2021}{2020}\)

hay \(x=-\dfrac{10101}{2020}\)

A = \(\dfrac{2^{2021}+1}{2^{2021}}\) =  \(\dfrac{2^{2021}}{2^{2021}}\)  + \(\dfrac{1}{2^{2021}}\) = 1 + \(\dfrac{1}{2^{2021}}\)

B = \(\dfrac{2^{2021}+2}{2^{2021}+1}\) = \(\dfrac{2^{2021}+1+1}{2^{2021}+1}\) = \(\dfrac{2^{2021}+1}{2^{2021}+1}\) +\(\dfrac{1}{2^{2021}+1}\) = 1 + \(\dfrac{1}{2^{2021}+1}\)

Vì \(\dfrac{1}{2^{2021}}\) > \(\dfrac{1}{2^{2021}+1}\) nên 1 + \(\dfrac{1}{2^{2021}}\) > 1 + \(\dfrac{1}{2^{2021}+1}\)

Vậy A > B 

Bài 1: Bạn xem lại đã viết đúng đề chưa vậy.

Bài 2:

$P=29-|16+3.2|+1=29-|22|+1=29-22+1=7+1=8$

2.

\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right).\left(2x+3\right)}=\frac{15}{93}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}\right)+\frac{1}{2}.\left(\frac{1}{7}-\frac{1}{9}\right)+...+\frac{1}{2}.\left(\frac{1}{2x+1}-\frac{1}{2x+3}\right)=\frac{15}{93}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2x+1}-\frac{1}{2x+3}\right)=\frac{15}{93}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{2x+3}\right)=\frac{15}{93}\)

\(\Rightarrow\frac{1}{3}-\frac{1}{2x+3}=\frac{15}{93}:\frac{1}{2}\)

\(\Rightarrow\frac{1}{3}-\frac{1}{2x+3}=\frac{10}{31}\)

\(\Rightarrow\frac{1}{2x+3}=\frac{1}{3}-\frac{10}{31}\)

\(\Rightarrow\frac{1}{2x+3}=\frac{1}{93}\)

\(\Rightarrow\)2x + 3 = 93

\(\Rightarrow\)2x = 93 - 3

\(\Rightarrow\)2x = 90

\(\Rightarrow\)x = 90 : 2 = 45

\(H=\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{33.37}\)

= \(\frac{3}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{33}-\frac{1}{37}\right)\)

= \(\frac{3}{4}\left(1-\frac{1}{37}\right)\)

= \(\frac{3}{4}.\frac{36}{37}=\frac{27}{37}\)

\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\)

\(=\frac{1}{3}+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+...+\left(\frac{1}{97}-\frac{1}{97}\right)-\frac{1}{99}\)

\(=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)

~ Hok tốt ~

\(\)

Viết thành 2 . (1/3.5 + 1/5.7 + 1/7.9 + ...+ 1/97.99

Tui hk bít nữa