1除以2*5+1除以3*6+1除以4*7+.+1除以7*10 简算

1÷(2×5)+1÷(3×6)+1÷(4×7)+……+1÷(7×10)=1/3 ×(1/2-1/5) +1/3×(1/3-1/6) +1/3×(1/4-1/7)+……+1/3×(1/7-1/10)=1/3 ×(1/2 -1/5 +1/3 -1/6 +1/4 -1/7 +……+1/7-1/10）=1/3 ×(1/2+1/3+1/4-1/8-1/9-1/10)...