a: 19191/2121<1<21/19

b: 62/51>1>56/45

Có : vì -22/103> -51/103

Suy ra : -22/44 > -51/103

-22/44 > -51/103

-22/44<-51/103

Ta có

\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{100}\right)-2\left(\frac{1}{2}+\frac{1}{4}+....+\frac{1}{100}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{100}\right)-1-\frac{1}{2}-\frac{1}{3}-....-\frac{1}{50}\)

\(=\frac{1}{51}+\frac{1}{52}+.....+\frac{1}{100}\)

=>.....

Ta có

11.2+12.3+....+199.100=1−12+13−14+....+199−11001.21​+2.31​+....+99.1001​=1−21​+31​−41​+....+991​−1001​

=(1+12+13+....+1100)−2(12+14+....+1100)=(1+21​+31​+....+1001​)−2(21​+41​+....+1001​)

=(1+12+13+....+1100)−1−12−13−....−150=(1+21​+31​+....+1001​)−1−21​−31​−....−501​

=151+152+.....+1100=511​+521​+.....+1001​
 

dấu*là gì vậy bạn

Giúp mình nhanh nha.

a, 2.[(-6² + 24) : 4] + 14

= 2.[(36 + 24) : 4] + 14

= 2.(60 : 4) + 14

= 2. 15 + 14

= 30 + 14

= 44

a : vì \(\dfrac{354}{758}< 1;\dfrac{123}{56}>1\\ \Rightarrow\dfrac{354}{758}< \dfrac{123}{56}\)

b:\(\dfrac{-18}{2021}< 0;\dfrac{75}{2022}>0\\ \Rightarrow\dfrac{-18}{2021}< \dfrac{75}{2022}\)

a)  Do 354/758<1 ;123/56>1

=>354/758<123/56

b) -18/2021<0;72/2022>0

=>-18/2021<72/2022

    -5 + (-37 - 45 + 51) - (-37 + 51)

=  -5  - 37 - 45 + 51 + 37 - 51

=  - (5 + 45) - (37 - 37) + (51 - 51)

= - 50 - 0 + 0

= - 50

  - (15 - 47 + 58) + (15 - 47 ) + 3

= - 15 + 47 - 58 + 15 - 47 + 3

= (-15 + 15) + (47 - 47) - (58 - 3)

= 0 + 0 - 55

= - 55

  (53 - 45 - 49) - (53 + 45 - 49)

= 53 -  45 - 49 - 53 - 45 + 49

= (53 - 53) + (-49 + 49) - (45 + 45)

= 0 + 0 - 90

= - 90 

    13 - 15 + 49 - 13 + 15 - 48

=  (13 - 13) + (-15 + 15) + (49 - 48)

= 0 + 0 + 1

=  1 

15+13 -15-13 +49-48

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

\(\)\(31^{31}< 3^{39}< 17^{39}\Rightarrow31^{31}< 17^{39}\)

Đính chính

\(2^{21}< 5^{21}< 5^{35}\Rightarrow2^{21}< 5^{35}\)

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