Đáp án:
`A =` $2^{100}$ `- 2`
Giải thích các bước giải:
`+ A = 2 + 2² + 2³ + ... +` $2^{99}$
`2A = 2 . ( 2 + 2² + 2³ + ... +` $2^{99}$ `)`
`2A = 2² + 2³ +` $2^{4}$ `+ ... +` $2^{100}$
`2A - A = ( 2² + 2³ +` $2^{4}$ `+ ... +` $2^{100}$ `) - ( 2 + 2² + 2³ + ... +` $2^{99}$ `)`
`A = 2² + 2³ +` $2^{4}$ `+ ... +` $2^{100}$ `- 2 - 2² - 2³ - ... -` $2^{99}$
`A = ( 2² - 2² ) + ( 2³ - 2³ ) + (` $2^{4}$ `-` $2^{4}$ `) + ... + (` $2^{99}$ `-` $2^{99}$ `) +` $2^{100}$ `- 2`
`A =` $2^{100}$ `- 2`
`+ 2 + 2² = 2 +` $2^{1+1}$ `= 2 . 1 +` $2^{1}$ . $2^{1}$ `= 2 . ( 1 +` $2^{1}$ `)`
