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\(\dfrac{5454}{5757}-\dfrac{171717}{191919}=\dfrac{1}{19}\)

\(\dfrac{2}{19}\)

Có: \(\dfrac{5454}{5757}-\dfrac{171717}{191919}.\dfrac{3}{4}+\dfrac{1}{4}:x=\dfrac{2}{5}\)

=> \(\dfrac{54.101}{57.101}-\dfrac{17.10101}{19.10101}.\dfrac{3}{4}+\dfrac{1}{4}:x=\dfrac{2}{5}\)

=> \(\dfrac{18}{19}-\dfrac{17}{19}.\dfrac{3}{4}+\dfrac{1}{4}:x=\dfrac{2}{5}\)

=> \(\dfrac{21}{76}+\dfrac{1}{4}:x=\dfrac{2}{5}\)

=> \(\dfrac{1}{4}:x=\dfrac{47}{380}\)

=> x = \(\dfrac{95}{47}\)

=>18/19-17/19*3/4+1/4:x=2/5

=>1/4:x=2/5-18/19+17/19*3/4=47/380

=>x=1/4:47/380=95/47

\(A=\frac{5454}{5757}-\frac{171717}{191919}=\frac{54}{57}-\frac{17}{19}=\frac{54}{57}-\frac{51}{57}=\frac{3}{57}=\frac{1}{19}\)

\(\frac{5454}{5757}-\frac{171717}{191919}=\frac{54x101}{57x101}-\frac{17x10101}{19x10101}=\frac{54}{57}-\frac{17}{19}=\frac{1}{19}\)

\(\frac{5454}{5757}-\frac{171717}{191919}=\frac{18.303}{19.303}-\frac{17.10101}{19.10101}=\frac{18}{19}-\frac{17}{19}=\frac{1}{19}\)

Ta có :

\(\frac{5454}{5757}=\frac{54.101}{57.101}=\frac{54}{57}\); \(\frac{171717}{191919}=\frac{17.10101}{19.10101}=\frac{17}{19}\)

Vậy \(\frac{54}{57}-\frac{17}{19}=\frac{1}{19}\)

\(\frac{5454}{5757}=\frac{54}{57}=\frac{18}{19};\frac{171717}{191919}=\frac{17}{19}\)

=> \(\frac{5454}{5757}=\frac{171717}{191919}=\frac{18}{19}-\frac{17}{19}=\frac{1}{19}\)

\(\dfrac{5454}{5757}-\dfrac{171717}{191919}=\dfrac{18\cdot3\cdot101}{19\cdot3\cdot101}-\dfrac{17\cdot10101}{19\cdot10101}=\dfrac{18}{19}-\dfrac{17}{19}=\dfrac{1}{19}\)

a,2/3 * 3/4 * 4/5 * 5/6

  Giản ước 3 với 3 , 4 với 4 , 5 với 5

=>2/3 * 3/4 * 4/5 * 5/6=2/6=1/3

b,5454/5757-171717/191919

=54/57-17/19

Quy đồng:54/57-(17*3/19*3)

               =54/57-51/57

               =3/57=1/19

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a,2/3 * 3/4 * 4/5 * 5/6

  Giản ước 3 với 3 , 4 với 4 , 5 với 5

=>2/3 * 3/4 * 4/5 * 5/6=2/6=1/3

b,5454/5757-171717/191919

=54/57-17/19

Quy đồng:54/57-(17*3/19*3)

               =54/57-51/57

               =3/57=1/19

a,2/3 * 3/4 * 4/5 * 5/6

  Giản ước 3 với 3 , 4 với 4 , 5 với 5

=>2/3 * 3/4 * 4/5 * 5/6=2/6=1/3

b,5454/5757-171717/191919

=54/57-17/19

Quy đồng:54/57-(17*3/19*3)

               =54/57-51/57

               =3/57=1/19

1) a) \(\frac{5454}{5757}-\frac{171717}{191919}=\frac{18\times3\times101}{19\times3\times101}-\frac{17\times10101}{19\times10101}=\frac{18}{19}-\frac{17}{19}=\frac{1}{19}\)

b) \(\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times....\times\frac{2021}{2020}=\frac{6\times7\times8\times...\times2021}{5\times6\times7\times...\times2020}=\frac{2021}{5}\)

2) \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}=2\times\frac{1}{6}+2\times\frac{1}{12}+2\times\frac{1}{20}+...+2\times\frac{1}{90}\)

\(=2\times\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)

\(=2\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\right)\)

\(=2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)=2\times\left(\frac{1}{2}-\frac{1}{10}\right)=2\times\frac{2}{5}=\frac{4}{5}\)

b)Vì \(a-1< a+1\)

=> \(\frac{1}{a-1}>\frac{1}{a+1}\)

1/ a x b = 1/a - 1/b 

đk : b - a = 1

Lời giải:

$S=1+5+5^4+5^6+5^8+....+5^{18}$

Tổng S có 10 số hạng, mỗi số hạng đều lẻ nên tổng S chẵn.

$\Rightarrow S\vdots 2$

$\Rightarrow 2S\vdots 4$

\(2929.57-5757.29\)

\(=29.101.57-57.101.29\)

\(=0\)