S = 1 + $2^{1}$ + $2^{2}$ + ... + $2^{100}$
2 . S = 2 . (1 + $2^{1}$ + $2^{2}$ + ... + $2^{100}$)
2 . S = 2 + $2^{2}$ + $2^{3}$ + ... + $2^{101}$
2 . S - S = (2 + $2^{2}$ + $2^{3}$ + ... + $2^{101}$) - (1 + $2^{1}$ + $2^{2}$ + ... + $2^{100}$)
S = $2^{101}$ - 1
Chúc học tốt!!!