so sánh hai phần số sau: a= 2525/2626 và b= 20232023/20242024
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\(\dfrac{112}{256}=\dfrac{112:16}{256:16}=\dfrac{7}{16}\)
\(\dfrac{25}{125}=\dfrac{25:25}{125:25}=\dfrac{1}{5}\)
\(\dfrac{37}{259}=\dfrac{37:37}{259:37}=\dfrac{1}{7}\)
\(\dfrac{506}{46}=11\)
\(\dfrac{77}{55}=\dfrac{77:11}{55:11}=\dfrac{7}{5}\)
\(\dfrac{20232023}{20242024}=\dfrac{20232023:10001}{20242024:10001}=\dfrac{2023}{2024}\)
Do đó: Không có cặp số phân số nào bằng nhau

Ta có : \(A\text{=}\dfrac{2023^{2023}}{2023^{2024}}\text{=}\dfrac{1}{2023}\)
và \(B\text{=}\dfrac{2023^{2022}}{2023^{2023}}\text{=}\dfrac{1}{2023}\)
\(\Rightarrow A\text{=}B\)
Ta có :
A=\(\dfrac{2023^{2023}}{2023^{2024}}\)=\(\dfrac{2023^{2022}.2023}{2023^{2023}.2023}\)=\(\dfrac{2023^{2022}}{2023^{2023}}\)
Mà B=\(\dfrac{2023^{2023}}{2023^{2024}}\)
Vậy A=B

\(\frac{25}{26}=\frac{2525}{2626}=\frac{252525}{262626}=\frac{25252525}{26262626}\)
Ta có:
2525/2626 = 25 × 101/26 × 101 = 25/26
252525/262626 = 25 × 10101/26 × 10101 = 25/26
25252525/26262626 = 25 × 1010101/26 × 1010101 = 25/26
Chứng tỏ các phân số trên đều = nhau

\(2023^{20}=\left(2023^2\right)^{10}=4092529^{10}\)
4092529<20232023
=>\(4092529^{10}< 20232023^{10}\)
=>\(2023^{20}< 20232023^{10}\)

2023²⁰²³ - 2023²⁰²² = 2023²⁰²².(2023 - 1) = 2023²⁰²².2022
2023²⁰²² - 2022²⁰²¹ = 2023²⁰²¹.(2023 - 1) = 2023²⁰²¹.2022
Do 2022 > 2021 ⇒ 2023²⁰²² > 2023²⁰²¹
⇒ 2023²⁰²².2022 > 2023²⁰²¹.2022
Vậy 2023²⁰²³ - 2023²⁰²² > 2023²⁰²² - 2023²⁰²¹

A = 19,19 x 2525,25
A = 19 x 1,01 x 25 x 101,01
B = 25,25 x 1919,19
B = 25 x 1,01 x 19 x 101,01
Vậy A = B
\(\text{+)}\)
\(A=19,19.2525,25\)
\(A=19.1,01.25.101,01\)
\(\text{+)}\)
\(B=25,25.1919,19\)
\(B=25.1,01.19.101,01\)
\(\Rightarrow A=B\)

1/3+1/15+1/35+1/63+1/99+1/143+1/195
=1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15
suy ra 2(1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15)
=2/1*3+2/3*5+2/5*7+2/7*9+2/9*11+2/11*13+2/13*15
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15
=1-1/15
=14/15
a=14/15 chia 2=7/15

\(A=\dfrac{1919}{100}\times\dfrac{252525}{100}=\dfrac{19\times101}{100}\times\dfrac{25\times10101}{100}=\dfrac{19\times25\times101\times10101}{100\times100}\)
\(B=\dfrac{2525}{100}\times\dfrac{191919}{100}=\dfrac{25\times101}{100}\times\dfrac{19\times10101}{100}=\dfrac{19\times25\times101\times10101}{100\times100}\)
Vậy \(A=B\)
A = 19,19 x 2525,25 = 19 x 1,01 x 25 x 101,01
B = 25,25 x 1919,19 = 25 x 1,01 x 19 x 101,01
Vậy A = B

Ta có \(\frac{25}{53}\)=\(\frac{25.101}{53.101}\)=\(\frac{2525}{5353}\)
\(\frac{25}{53}\)=\(\frac{25.10101}{53.10101}\)=\(\frac{252525}{535353}\)
Help tớ
a>b