2的n次方+2的n-1次方+·····+2+1

问题描述:

2的n次方+2的n-1次方+·····+2+1

=1×(2的(n+1)次方 -1) /(2-1)
=2的(n+1)次方 -1

==2的n+1次方-1
2^(n+1)-1

令s=2^n+2^(n-1)+.+2+1
2s=2^(n+1)+2^n+.+2^2+2^1
2s-s=2^(n+1)-1
s=2^(n+1)-1

=2^(n+1)-1