Ta có:
` A = 2^{100} - 2^{99} - 2^{98} - ... - 2^2 - 2 - 1 `
` <=> 2A = 2^{101} - 2^{100} - 2^{99} - ... - 2^3 - 2^2 - 2 `
` <=> 2A - A = (2^{101} - 2^{100} - 2^{99} - ... - 2^3 - 2^2 - 2) - (2^{100} - 2^{99} - 2^{98} - ... - 2^2 - 2 - 1) `
` <=> A = 2^{101} - 2^{100} - 2^{99} - ... - 2^3 - 2^2 - 2 - 2^{100} + 2^{99} + 2^{98} + ... + 2^2 + 2 + 1 `
` <=> A = 2^{101} - (2^{100} + 2^{100}) + (2^{99} - 2^{99}) + ... + (2 - 2) + 1 `
` <=> A = 2^{101} - (2^{100}.2) + 1 `
` <=> A = 2^{101} - 2^{101} + 1 `
` <=> A = 0 + 1 = 1 `
Vậy ` A = 1 `