Đặt A=$2^{2}$ +$2^{2}$ +$2^{3}$ +$2^{4}$ +$2^{5}$ +....+$2^{2019}$
=>2A=$2^{3}$ +$2^{3}$ +$2^{4}$ +$2^{5}$ +$2^{6}$ +....+$2^{2020}$
=>2A-A=($2^{2}$ +$2^{2}$ +$2^{3}$ +$2^{4}$ +$2^{5}$ +....+$2^{2019}$ )-($2^{3}$ +$2^{3}$ +$2^{4}$ +$2^{5}$ +$2^{6}$ +....+$2^{2020}$)
A=$2^{3}$+ $2^{2020}$-$2^{2}$- $2^{2}$
= $2^{3}$-$2^{2}$- $2^{2}$+ $2^{2020}$
=0+ $2^{2020}$
= $2^{2020}$
vậy tổng $2^{2}$ +$2^{2}$ +$2^{3}$ +$2^{4}$ +$2^{5}$ +....+$2^{2019}$ dưới dạng lũy thừa của 2 là $2^{2020}$
