设k为大于1的正整数则1/((k-1)k(k+1))=k/((k-1)k*k(k+1))=(k(k+1)-k(k-1))/2((k-1)k*k(k+1))=(1/(k(k-1))-1/(k(k+1)))/2所以原式=(1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+……+1/(20*21)-1/(21*22))/2=(1/(1*2)-1/(21*22)...