S = 1 + 2 + 22 + 23 + ... + 22019
2S = 2(1 + 2 + 22 + 23 + ... + 22019)
2S = 2 + 22 + 23 + ... + 22020
2S - S = (2 + 22 +23 + ... + 22020) - (1 + 2 + 22 + ... + 22019)
S = 22020 - 1
S = 1 +2 + 22 + 23 + ... + 22019
2S = 2(1 + 2 + 22 + ... + 22019)
2S = 2 + 22 + 23 + ... + 22020
2S - S = (2 + 22 + 23 + ... + 22020) - (1 + 2 + 22 + ... + 22019)
S = 22020 - 1
S=1+2+22+23+...+22019
2S=2+22+23+...+22019+22020
2S-S=22020-1
S=22020-1
\(2S=2\left(1+2+...+2^{2019}\right)\)
\(=2^2+...+2^{2019}\)
\(2S-S=2^{2019}-1\)
\(\Rightarrow S=2^{2019}-1\)