Bạn tham khảo :
Đặt $A = 1+2+2^2+ 2^3 + ....+ 2^{99}$
$2A = 2 + 2^2 + 2^3 + 2^4 + ... + 2^{100}$
$2A - A = (2 + 2^2 + 2^4 + ... + 2^{100}) - ( 1+2+2^2+ 2^3 + ....+ 2^{99})$
$A = (2-2) + (2^2 - 2^2) + (2^3 - 2^3) + (2^4 - 2^4) + ... + ( (2^{100} - 1)$
$A = 2^{100} - 1$
Vậy $A = 2^{100} - 1 =2^{100} - 1$
⇒ $1+2+2^2+ 2^3 + ....+ 2^{99} = 2^{100} - 1$
