Question

A=1+2^1+2^2+2^3+....+2^100

B=2^101

So sánh A và B

Answer 1

A=1+2¹+2²+2³+...+2¹⁰⁰

2A=2+2²+2³+2⁴+...+2¹⁰¹

2A-A=2¹⁰¹-1

A=2¹⁰¹-1

Ta có 2¹⁰¹>2¹⁰¹-1 nên B>A

Answer 2

2A=2+2^2+2^3+2^4+....+2^101

=> 2A-A=(2+2^2+2^3+2^4+....+2^101)-(1+2+2^2+2^3+...+2^100)

<=> A=2^101-1 > B=2^101

Answer 3

2A=2+2^2+...+2^101

=>2A-A=(2+2^2+...+2^101)-(1+2+2^2+...+2^100)

=> A=2^101-1<2^101=B

vậy a<b

Answer 4

A=2^0+2^1+2^2+2^3+2^4+...+2^100

2A=2^1+2^2+2^3+2^4+2^5+...+2^100+2^101

2A-A=(2^1+2^2+2^3+2^4+2^5+...+2^100+2^101)-(2^0+2^1+2^2+2^3+2^4+...+2^100)

\(\Rightarrow\)A=2^101-1

Ta thấy A=2^101-1<2^101.Vậy A<B