Question

在计算2^100-2^99时可用如下方法进行:2^100-2^99=2*2^99-1*2^99=92-1)*2^99=2

Answer 1

答：

2^50-2^49+2^48-……-2^3+2^2-2^1

=(2-1)*2^49+(2-1)*2^47+.+(2-1)*2^1

=2^49+2^47+.+2^1

=2*(4^25-1)/(4-1)

=(2/3)*(4^25-1)