(1/2+1/3+1/4+```+1/20)+(2/3+2/4+```+2/20)+(3/4+3/5+···3/20)+
1个回答

(1/2+1/3+1/4+...+1/20)+(2/3+2/4+...+2/20)+(3/4+3/5+...+3/20)+...+(18/19+18/20)+19/20

[1+2+3+...+(n-1)]/n=n(n-1)/2n=(n-1)/2

(1/2+1/3+1/4+...+1/20)+(2/3+2/4+2/5+...+2/20)+(3/4+3/5+...+3/20)+...+(18/19+18/20)+19/20

=1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/20+2/20+3/20+...+19/20)

=(2-1)/2+(3-1)/2+(4-1)/2+...+(20-1)/2

=(1+2+3+...+20)/2

=20*21/4

=5*21

=105