1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)=1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)=
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![1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)=1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)=](/uploads/image/z/9328070-38-0.jpg?t=1%E5%8F%881%2F2%2B2%E5%8F%881%2F4%2B3%E5%8F%881%2F8%2BL+L%2B%28n%2B1%2F2%5En%29%3D1%2B1%2F%281%2B2%29%2B1%2F%281%2B2%2B3%29%2B...%2B1%2F%281%2B2%2B3%2B...%2Bn%29%3D)
1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)=1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)=
1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)=
1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)=
1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)=1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)=
1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)
=(1+2+3+...+n)+(1/2+1/4+1/8+...+1/2^n)
=n(n+1)/2+(1/2^n-1)
1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)
1+2+3+.+n=n(n+1)
1/(1+2+3+...+n)=1/n(n+1)=1/n-1/(n+1)
所以
原式=1+1/1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/(n-1)
=1+1+1/n
=2+1/n