计算
问题描述：
计算
1/1×2)＋1/(2×3)＋1/(3×4)＋1/(4×5)＋.＋1/(42×43)＝?
答
1/(1×2) = 1/1 - 1/21/(2×3) = 1/2 - 1/3...1/(42×43) = 1/42 - 1/43所以：1/1×2)＋1/(2×3)＋1/(3×4)＋1/(4×5)＋.＋1/(42×43)=(1/1 - 1/2) + (1/2 - 1/3) + ...+ (1/42 - 1/43)=1 - 1/43= 42/43