Question

1×2×3×4分之1加2乘三乘四分之一加到7乘八乘九乘十分之一？

Answer 1

分数裂项题目。分母4个连乘要化成两个分数3个连乘的差
1/1x2x3x4=1/3(1/1x2x3-1/2x3x4)
1/2x3x4x5=1/3(1/2x3x4-1/3x4x5)
.......
原式=1/3(1/1x2x3-1/2x3x4+1/2x3x4-1/3x4x5+...+1/7x8x9-1/8x9x10)
=1/3(1/1x2x3-1/8x9x10)
=1/3(1/6-1/720)
=1/3 x 119/720
=119/2160
望采纳，谢谢

Answer 2

1/(1×2×3×4)+1/(2×3×4)+1/(7×8×9×10)
=2(7×8×9×10)+(2×3×4)/(2×3×4)(7×8×9×10)
=10104/120960
=421/5040