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2m2cm = 202 cm 

4025g = 4,025 kg

\(2\dfrac{2}{100}=\dfrac{202}{100}m\)

\(\dfrac{425}{100}m\)

a, \(\dfrac{14}{5}.x-50=34\\ =>\dfrac{14}{5}.x=34+50=84\\ =>x=84:\dfrac{14}{5}=30\)

b, \(\left(25\%-2\dfrac{1}{2}\right).2x-\dfrac{5}{4}.2^4=\dfrac{525}{100}\\ < =>\left(\dfrac{1}{4}-\dfrac{5}{2}\right).2x-\dfrac{5}{4}.16=\dfrac{525}{100}\\ < =>-\dfrac{9}{4}.2x-20=\dfrac{525}{100}\\ < =>-\dfrac{9}{2}x-20=\dfrac{525}{100}\\ =>-\dfrac{9}{2}x=\dfrac{525}{100}+20=\dfrac{101}{4}\\ =>x=\dfrac{\dfrac{101}{4}}{-\dfrac{9}{2}}=-\dfrac{101}{18}\)

24 tháng 5 2017

bạn có thể ghi cho mình rõ hơn một chút đi nhưng k sao cảm ơn bạnNguyễn Trần Thành Đạt nha

a: \(A=\left(100^2-1\right)\left(100^4+100^2+1\right)=100^6-1\)

b: \(B=\left(\dfrac{1}{5}a-b\right)\left(\dfrac{1}{25}a^2+\dfrac{1}{5}ab+b^2\right)=\left(\dfrac{1}{5}a\right)^3-b^3=\dfrac{1}{125}a^3-b^3\)

c: \(C=\left(2+a\right)\left(4-2a+a^2\right)\left(2-a\right)\left(4+2a+a^2\right)\)

\(=\left(8+a^3\right)\left(8-a^3\right)=64-a^6\)

b: \(\Leftrightarrow\left(\dfrac{29-x}{21}+1\right)+\left(\dfrac{27-x}{23}+1\right)+\left(\dfrac{25-x}{25}+1\right)+\left(\dfrac{23-x}{27}+1\right)+\left(\dfrac{21-x}{29}+1\right)=0\)

=>50-x=0

hay x=50

c: \(\Leftrightarrow\dfrac{x-2}{2001}+1=\dfrac{x-1}{2002}+\dfrac{x}{2003}\)

\(\Leftrightarrow\left(\dfrac{x-2}{2001}-1\right)=\left(\dfrac{x-1}{2002}-1\right)+\left(\dfrac{x}{2003}-1\right)\)

=>x-2003=0

hay x=2003

AH
Akai Haruma
Giáo viên
29 tháng 11 2023

Lời giải:

\(A=\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}\)

\(3A=1-\frac{2}{3}+\frac{3}{3^2}-\frac{4}{3^3}+...+\frac{99}{3^{98}}-\frac{100}{3^{99}}\)

\(4A=A+3A=1-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+....-\frac{1}{3^{99}}-\frac{100}{3^{100}}\)

\(12A=3-1+\frac{1}{3}-\frac{1}{3^2}+....-\frac{1}{3^{98}}-\frac{100}{3^{99}}\)

\(\Rightarrow 16A=12A+4A=3-\frac{101}{3^{99}}-\frac{100}{3^{100}}<3\)

\(\Rightarrow A< \frac{3}{16}\)

27 tháng 5 2017

\(A=\left[\dfrac{1}{100}-1^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{3}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)\(=\left[\dfrac{1}{100}-1^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{3}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{10}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)\(\dfrac{1}{100}-\left(\dfrac{1}{10}\right)^2=\dfrac{1}{100}-\dfrac{1}{100}=0\)

\(\Rightarrow A=0\)

27 tháng 5 2017

\(\left(\dfrac{1}{100}-1^2\right)\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)

\(=\left(\dfrac{1}{100}-1^2\right)\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{10}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)

\(=\left(\dfrac{1}{100}-1^2\right)\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right]...0...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)

\(=0\)

Vậy...

AH
Akai Haruma
Giáo viên
26 tháng 6 2023

Lời giải:

$M=\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+....+\frac{100}{3^{100}}$

$3M=1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{100}{3^{99}}$

$\Rightarrow 2M=3M-M=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}-\frac{100}{3^{100}}$

$2M+\frac{100}{3^{100}}=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}$

$3(2M+\frac{100}{3^{100}})=3+1+\frac{1}{3}+...+\frac{1}{3^{98}}

$\Rightarrow 2(2M+\frac{100}{3^{100}})=3(2M+\frac{100}{3^{100}})-(2M+\frac{100}{3^{100}})=2-\frac{1}{3^{99}}$

$M=\frac{1}{2}-\frac{1}{4.3^{99}}-\frac{50}{3^{100}}<\frac{1}{2}< \frac{3}{4}$ 
Ta có đpcm.

24 tháng 2 2021

`a,3/10=0,3`

`3/100=0,03`

`4 25/100=4 1/4=4,25`

`2002/1000=2,002`

`b,1/4=0,25`

`3/5=0,6`

`7/8=0,875`

`1 1/2=1,5`

24 tháng 2 2021

a) Biểu diễn bằng số thập phân: 0,3; 0,03; 4,25; 2,002

b) Biểu diễn bằng số thập phân: 

\(\dfrac{1}{4}=\dfrac{25}{100}=0,25\\ \dfrac{3}{5}=\dfrac{6}{10}=0,6\\ \dfrac{7}{8}=\dfrac{875}{1000}=0,875\\ 1\dfrac{1}{2}=\dfrac{3}{2}=\dfrac{15}{10}=1,5\)