Question

So sánh A vàB

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

B=5.4^4

Answer 1

Tính A=\(1+2^2+2^3+..+2^{99}\)

=> 2A-A=A=\(\left(2+2^2+2^3+..+.2^{100}\right)-\left(1+2+2^2+..+2^{99}\right)=2^{100}-1\)

ta có B= \(5.4^4< 8.4^4=2^{11}< 2^{100}-1\)

=> A>B

Answer 2

Ta có : A=1+2+2^2+2^3+...+2^99

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

A=2^100-1