Ta có:
\(A=2^0+2^1+2^2+...+2^{40}\)

\(\Rightarrow2A=2^1+2^2+2^3+...+2^{41}\)

\(\Rightarrow2A-A=\left(2^1+2^2+2^3+...+2^{41}\right)-\left(2^0+2^1+...+2^{40}\right)\)

\(\Rightarrow A=2^{41}-2^0\)

\(\Rightarrow A=2^{41}-1\)

Vì \(2^{41}-1< 2^{41}\) nên A < B

Vậy A < B

2xA- A= A= 2 ^ 41 - 1 < B

Ngắn gọn, hàm xúc, dễ hiểu

b . <

a thì vẫn chưa ra

a) Lấy 2A - A ,được 2^51 - 1 < 2^51

=> A < B

b) 2^300 = (2^3)^100 = 8^100

    3^200 = (3^2)^100 = 9^100

=> 2^300 < 3^200 

2²⁷=(2³)⁹=8⁹

3¹⁸=(3²)⁹=9⁹

vì 9>8=>9⁹>8⁹

A = 2⁰ + 2¹ + 2² + .. + 2⁵⁰

2A = 2 + 2² + 2³ + ... + 2⁵¹

2A - A = A = 2⁵¹ - 2 < 2⁵¹ = B

=> A < B 

Ta có 2A=2¹+2²+2³+...+2⁵¹

=> A= (2¹+2²+2³+...+2⁵¹) - ( 2⁰⁺2¹+2²+2³+...+2⁵⁰)

=> A= 2⁵¹ - 2⁰ < 2⁵¹=B

=> A<B

\(A=1+2+2^2+2^3+...+2^{50}\)

\(2A=2+2^2+2^3+2^4+....+2^{51}\)

\(=>2A-A=\left(2+2^2+2^3+2^4+...+2^{51}\right)-\left(1+2+2^2+2^3+....+2^{50}\right)\)

\(=>A=2^{51}-1< 2^{51}=B=>A< B\)

A = 2⁰ + 2¹ + 2² + 2^{3 +}...+2⁵⁰

=>2A=2( 2⁰ + 2¹ + 2² + 2^{3 +}...+2⁵⁰)=2¹+2²+2³+...+2⁵¹

=>2A-A=2¹+2²+2³+...+2⁵¹-(2⁰ + 2¹ + 2² + 2^{3 +}...+2⁵⁰)

A=2¹+2²+2³+...+2⁵¹-2⁰-2¹-2²-2³-...-2⁵⁰

=2⁵¹-2⁰

=2⁵¹-1<2⁵¹

=>A<B

A=(2^51)-1;B=2^51

suy ra A<B

so sanh a*b /a^2+b^2 va a^2+b^2/(a+b)^2