Question

rút gọn:  \(1+2+2^2+2^3+2^4+...+2^{2014}\)

Answer 1

1+2+2²+2³+2⁴+...+2²⁰¹⁴

=2-1+2²-2+2³-2²+2⁴-2³+2⁵-2⁴+...+2²⁰¹⁵-2²⁰¹⁴

=2²⁰¹⁵-1

Answer 2

Đăt S = 1 + 2^2 +.. + 2^2014

     2S = 2 + 2^3  + ... + 2 ^2014 + 2^2015

2S - S = 2 + 2 ^3 + ..  + 2^2014 + 2^2015 - 1 - 2 - 2^3 -... - 2^2014

=> S = 2^2015 - 1