遗失的心跳:从2的1次方加到2的100次方是多少
来源:百度文库 编辑:中科新闻网 时间:2024/06/01 10:38:14
2+2^2+2^3+...+2^100
=2+2+2^2+2^3+...+2^100-2
=2^2+2^2+2^3+...+2^100-2
=2^3+2^3+...+2^100-2
=...
=2^100+2^100-2
=2^101-2
2(2^100-1)
2+2^2+2^3+...+2^100
=2+2+2^2+2^3+...+2^100-2
=2^2+2^2+2^3+...+2^100-2
=2^3+2^3+...+2^100-2
=...
=2^100+2^100-2
=2^101-2
2(2^100-1)