2^49+2^48+2^47+2^46…+2+1

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2^49+2^48+2^47+2^46…+2+12^49+2^48+2^47+2^46…+2+12^49+2^48+2^47+2^46…+2+1前两个数:2^50=2*2^492^50-2^49=2*

2^49+2^48+2^47+2^46…+2+1
2^49+2^48+2^47+2^46…+2+1

2^49+2^48+2^47+2^46…+2+1
前两个数:
2^50=2*2^49
2^50-2^49=2*(2^49)-2^49=(2-1)2^49=2^49
同理
到第三个:
2^49-2^48=2^48
...
到倒数第二个:
2^2-2=2
最后一个:
2-1=1

t=
2^49+2^48+2^47+2^46…+2+1
2t=
2^50+2^49+2^48+2^47+2^46…+2
相减t=2^50-1

设原式=a 则2a=2^50+2^49+省略号+2+1 2a-a=2^ 50-1=a