Question

1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)=

Answer 1

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