Question

巧算1/2 2/2x3十3/2x3x4十4/2x3x4x5十5/2x3x4x5x6

• 你的回答被采纳后将获得：
• 系统奖励15（财富值+成长值）+难题奖励30（财富值+成长值）

Answer 1

1/1*2+2/1*2*3+3/1*2*3*4+4/1*2*3*4*5+5/1*2*3*4*5*6+6/1*2*3*4*5*6*7
=1-1/1*2+1/1*2-1/1*2*3+1/1*2*3-1/1*2*3*4+1/1*2*3*4-1/1*2*3*4*5+1/1*2*3*4*5-1/1*2*3*4*5*6+61//1*2*3*4*5*6-1/1*2*3*4*5*6*7
=1-1/1*2*3*4*5*6*7
=1-1/5040
=5039/5040

Answer 2

裂项法：
1/2+2/2x3十3/2x3x4十4/2x3x4x5十5/2x3x4x5x6
=1-1/2+1/2-1/2x3十1/2x3-1/2×3x4十1/2x3x4-1/2×3×4×5十1/2x3x4x5-1/2×3×4×5x6
=1-1/2×3×4×5×6
=1-1/720
=719/720