Question

So sánh A và B

A = 2⁰ + 2¹ + 2² + 2^{3 +}...+2⁵⁰

B = 2⁵¹

Answer 1

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

Answer 2

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

suy ra A<B

Answer 3

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

Answer 4

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

Answer 5

2A= 2^1 + 2^2 +... +2^51

2A-A= (2^1 + 2^2+... + 2^51)- (2^0 +2^1 +...+2^50)

A=2^51-2^0=2^51-0<2^51=B

Vậy A<B (ĐPCM)

Answer 6

\(A=2^0+2^1+2^2+........+2^{50}\)

\(\Leftrightarrow2A=2.\left(2^0+2^1+2^2+............+2^{50}\right)\)

\(\Leftrightarrow2A=2^1+2^2+2^3+............+2^{51}\)

\(\Leftrightarrow2A-A=\left(2^1+2^2+2^3+.............+2^{51}\right)-\left(2^0+2^1+..............+2^{50}\right)\)

\(\Leftrightarrow A=2^{51}-2^0=2^{51}-1< 2^{51}\Leftrightarrow A< B\)

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