\(=\frac{-\frac{1}{9}+1-\frac{2}{10}+1-\frac{3}{11}+1-...-\frac{92}{100}+1}{\frac{1}{9}+\frac{1}{10}+...+\frac{1}{100}}\)

\(=\frac{\frac{8}{9}+\frac{8}{10}+\frac{8}{11}+...+\frac{8}{100}}{\frac{1}{9}+\frac{1}{10}+...+\frac{1}{100}}\)

\(=\frac{8\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{100}\right)}{\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{100}}\)

= 8

dễ lắm nhưng bây h mình k có thời gian để giải 

Ta có: B > 1

=> B = \(\frac{2^{10}-1}{2^{10}-3}>\frac{2^{10}-1+2}{2^{10}-3+2}=\frac{2^{10}+1}{2^{10}-1}=A\)

Vậy A < B

\(\frac{2^{10}+1}{2^{10}-1}=\frac{2^{10}-1+2}{2^{10}-1}=1+\frac{2}{2^{10}-1}\)

\(\frac{2^{10}-1}{2^{10}-3}=\frac{2^{10}-3+2}{2^{10}-3}=1+\frac{2}{2^{10}-3}\)

Nhận thấy: \(\frac{2}{2^{10}-3}>\frac{2}{2^{10}-1}\) do 2¹⁰-3 < 2¹⁰-1

Vậy: \(\frac{2^{10}-1}{2^{10}-3}>\frac{2^{10}+1}{2^{10}-1}\)

Ta có : \(\frac{a}{b}>1\Rightarrow\frac{a}{b}>\frac{a+n}{b+n}\)

Nên : \(B=\frac{2^{10}-1}{2^{10}-3}>\frac{2^{10}-1+2}{2^{10}-3+2}=\frac{2^{10}+1}{2^{10}-1}\)

Good

\(\text{A = }\frac{\text{-1}}{\text{2011}}-\frac{\text{3}}{\text{11}^2}-\frac{\text{5}}{\text{11}^2.\text{11}}-\frac{\text{7}}{\text{11}^2.\text{11}^2}=\text{ }\frac{\text{-1}}{\text{2011}}-\frac{\text{1}}{\text{11}^2}.\left(3-\frac{\text{5}}{\text{11}}-\frac{\text{7}}{\text{11}^2}\right)\)

\(\text{B = }\frac{\text{-1}}{\text{2011}}-\frac{7}{\text{11}^2}-\frac{5}{\text{11}^2.\text{11}}-\frac{3}{\text{11}^2.\text{11}^2}=\frac{\text{-1}}{\text{2011}}-\frac{\text{1}}{\text{11}^2}.\left(7-\frac{5}{\text{11}}-\frac{3}{\text{11}^2}\right)\)

\(\text{Vì }3-\frac{\text{5}}{\text{11}}-\frac{\text{7}}{\text{11}^2}< 7-\frac{5}{\text{11}}-\frac{3}{\text{11}^2}\)

\(\Rightarrow\frac{\text{-1}}{\text{2011}}-\frac{\text{1}}{\text{11}^2}.\left(3-\frac{\text{5}}{\text{11}}-\frac{\text{7}}{\text{11}^2}\right)>\frac{\text{-1}}{\text{2011}}-\frac{\text{1}}{\text{11}^2}.\left(7-\frac{5}{\text{11}}-\frac{3}{\text{11}^2}\right)\)

=> A > B

Vậy A > B

2³⁵⁰<3²¹⁰

Vì cơ số lớn thì lũy thừa đó cũng lớn

Ủng hộ em nha

 3^210 < 2^350

Ủng hộ đê 

2^350=(2^5)^70=32^70(1)

3^210=(3^3)^70=27^70(2)

Từ 1 và 2 suy ra 2^350>3^210

Câu 1 tự làm nhé! Đưa về cùng số mũ mà so sánh

Câu 2 : 

<=> x.2 + x.4 + x.8 +.......+ x.512 = 511

<=> x.( 2+4+8+....+512) = 2⁹-1

<=> x. (2¹⁰-2) = 2⁹-1

<=> x = 2⁹-1 / 2¹⁰-2

<=> x = 2⁹-1/2(2⁹-1) = 1/2 = 0,5

=> x = 0,5 nhé!

Xx2 + Xx4 + Xx8 + ....+ Xx512 = 511

Xx(2 + 4 + 8 + ... + 512 ) = 511

Xx73 = 511

X = 511 :73

X = 7

mình ko chắc đúng đâu

Câu 2

x(  1 / 2+1 / 4 + 1 / 8 +1 / 16....+1 / 512 )=511

x( 3/4 + 1/8 + 1/ 16 ....+1 / 512)=511               

x(7/8+1/16+....1/512)=511

x (511/512)=511           { quy luật (a-1)/a}

x=512