a ) − 4 5 > − 1 b ) 1 24 < 1

Đáp án cần chọn là: D

A = 2 5 .7 + 2 5 2 5 .5 2 − 2 5 .3 = 2 5 . ( 7 + 1 ) 2 5 . ( 5 2 − 3 ) = 2 5 . ( 7 + 1 ) 2 5 . ( 25 − 3 ) = 2 5 .8 2 5 .22 = 8 22 = 4 11 B = 3 4 .5 − 3 6 3 4 .13 + 3 4 = 3 4 . ( 5 − 3 2 ) 3 4 . ( 13 + 1 ) = 3 4 . ( 5 − 9 ) 3 4 .14 = 3 4 . ( − 4 ) 3 4 .14 = − 4 14 = − 2 7

MSC = 77

4 11 = 4.7 11.7 = 28 77 ; − 2 7 = − 2.11 7.11 = − 22 77

Do đó  − 22 77 < 28 77 < 1  hay B < A < 1

a ) 7 4 > 1 b ) 20 9 <3

a ) − 1 10 < 1. b ) 39 20 < 2. c ) − 1 20 > − 11 40 . d ) 5 9 > 2 9

Ta có: \(a=\frac13+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+\cdots+\frac{2022}{3^{2022}}\)

=>\(3a=1+\frac23+\frac{3}{3^2}+\frac{4}{3^3}+\cdots+\frac{2022}{3^{2021}}\)

=>\(3a-a=1+\frac23+\frac{3}{3^2}+\cdots+\frac{2022}{3^{2021}}-\frac13-\frac{2}{3^2}-\frac{3}{3^3}-\cdots-\frac{2022}{3^{2022}}\)

=>\(2a=1+\frac13+\frac{1}{3^2}+\cdots+\frac{1}{3^{2021}}-\frac{2022}{3^{2022}}\)

Đặt \(b=\frac13+\frac{1}{3^2}+\cdots+\frac{1}{3^{2021}}\)

=>\(3b=1+\frac13+\cdots+\frac{1}{3^{2020}}\)

=>\(3b-b=1+\frac13+\ldots+\frac{1}{3^{2020}}-\frac13-\frac{1}{3^2}-\cdots-\frac{1}{3^{2021}}\)

=>\(2b=1-\frac{1}{3^{2021}}=\frac{3^{2021}-1}{3^{2021}}\)

=>\(b=\frac{3^{2021}-1}{2\cdot3^{2021}}\)

Ta có: \(2a=1+\frac13+\frac{1}{3^2}+\cdots+\frac{1}{3^{2021}}-\frac{2022}{3^{2022}}\)

=>\(2a=1+\frac{3^{2021}-1}{2\cdot3^{2021}}-\frac{2022}{3^{2022}}=1+\frac{3^{2022}-3-4044}{2\cdot3^{2022}}=1+\frac12-\frac{4047}{2\cdot3^{2022}}\)

=>\(2a<\frac32\)

=>\(a<\frac34\)

a)  − 1 20 > − 11 40

b)  5 9 > 2 9

a) x > y       b) x > y

a ) − 1 < 1 ; b ) 9 15 > 7 15 ; c ) − 1 2 > − 7 12 ; d ) 71 20 < 4

34^34-34³³>34³⁵ -34³⁴

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