Question

A=1+2+2^2+2^3+...+2^99

B=2^100

so sánh A và B

Answer 1

A = 1 + 2 + 2² + 2³ + ... + 2⁹⁹

2A = 2 . (1 + 2 + 2² + 2³ + ... + 2⁹⁹)

2A = 2 + 2² + 2³ + 2⁴ + ... + 2¹⁰⁰

2A - A = (2 + 2² + 2³ + 2⁴ + ... + 2¹⁰⁰) - (1 + 2 + 2² + 2³ + ... + 2⁹⁹)

A = 2¹⁰⁰ - 1

Vì 2¹⁰⁰ - 1 < 2¹⁰⁰ => A < B

Answer 2

2.A=2.(1+2+2^2+2^3+....+2^99)

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

2.A-A=2+2^2+2^3+2^4+....2^100-(1+2+2^2+2^3+....+2^99)

A=2^100-1

B=2^100

SUY RA :A<B 

vì 2^100-1<2^100

Answer 3

A=1+2+2²+2³+...+2⁹⁹

=>2A=2+2²+2³+2⁴+...+2¹⁰⁰

=>2A-A=2+2²+2³+2⁴+...+2¹⁰⁰-1-2-2²-2³-...-2⁹⁹

=>A=2¹⁰⁰-1<2¹⁰⁰=B(đcpm)

Vậy A<B