Question

so sánh:

  A=1+2+2² + ......+ 2⁵⁰;   B= 2⁵¹

Answer 1

Ta có:

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

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

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

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

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

Vì \(2^{51}-1< 2^{51}\) nên A<B

Answer 2

a, Lấy A-B
= 1+2+....+2^49+2^50 - 2^51
= 1+2+....+ 2^49+ 2^50 . ( 1-2)
= 1+2+.....+ 2^49 - 2^50
= 1+2+....+2^48 - 2^49
......
......
=   1+2+2^2-2^3
=   1+2-2^2
=   1-2 = -1 <0 ===>       A<B

Answer 3

a, Lấy A-B

= 1+2+....+2^49+2^50 - 2^51
= 1+2+....+ 2^49+ 2^50 . ( 1-2)
= 1+2+.....+ 2^49 - 2^50
= 1+2+....+2^48 - 2^49
......
......
=   1+2+2^2-2^3
=   1+2-2^2
=   1-2 = -1 <0 ===>       A<B

Answer 4

\(\text{Ta có: }\)\(A=1+2+2^2+...+2^{50}\)

\(\Rightarrow2A=2\left(1+2+2^2+...+2^{50}\right)\)

\(\Rightarrow2A=2+2^2+2^3+...+2^{51}\)

\(\Rightarrow2A-A=2^{51}-1\)

\(\Rightarrow A=2^{51}-1\)

Mà B = 2⁵¹ nên A < B