﹙1+1/1*3﹚×﹙1+1/2*4﹚×﹙1+1/3*5)……(以此类推)×﹙1+1/8*10﹚
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 02:36:29
![﹙1+1/1*3﹚×﹙1+1/2*4﹚×﹙1+1/3*5)……(以此类推)×﹙1+1/8*10﹚](/uploads/image/z/766442-2-2.jpg?t=%EF%B9%991%2B1%EF%BC%8F1%2A3%EF%B9%9A%C3%97%EF%B9%991%2B1%EF%BC%8F2%2A4%EF%B9%9A%C3%97%EF%B9%991%2B1%2F3%2A5%EF%BC%89%E2%80%A6%E2%80%A6%28%E4%BB%A5%E6%AD%A4%E7%B1%BB%E6%8E%A8%EF%BC%89%C3%97%EF%B9%991%2B1%EF%BC%8F8%2A10%EF%B9%9A)
﹙1+1/1*3﹚×﹙1+1/2*4﹚×﹙1+1/3*5)……(以此类推)×﹙1+1/8*10﹚
﹙1+1/1*3﹚×﹙1+1/2*4﹚×﹙1+1/3*5)……(以此类推)×﹙1+1/8*10﹚
﹙1+1/1*3﹚×﹙1+1/2*4﹚×﹙1+1/3*5)……(以此类推)×﹙1+1/8*10﹚
小学奥数这么难啊.
﹙1+1/1*3﹚× ﹙1+1/2*4﹚×﹙1+1/3*5)……(以此类推)×﹙1+1/8*10﹚
=4/3 × 9/8 × 16/15 × 25/24 +……+81/80
=2²×3²×4²×5²×……×9²/[(2²-1)×(3²-1)×(4²-1)×(5²-1)×……×(9²-1)]
分母=
[(2²-1)×(3²-1)×(4²-1)×(5²-1)×……×(9²-1)]=1×3 × 2×4 × 3×5 × 4 × 6×5×7×6×8×7×9× 8×10
=1×2×3²×4²×……×8²×9×10
分子分母约去3²×4²×……×8²后
=2²×9²/1×2×9×10
=2×9/10
=9/5
4/3 * 9/8 * 16/15 * 25/24 * 36/35 * 49/48 * 64/63 * 81/80
一通 约分 得1.8
(1+1/1*3)x(1+1/2*4)x(1+1/3*5).........x(1+1/8*10)
=(2²/1*3)x(3²/2*4)x(4²/3*5)x(5²/4*6)......x(9²/8*10)
=(2²*3²*4²*5²......*9²)/(1*2*3²*4².....8²*9*10)
=(2²*9²)/(1*2*9*10)
=2*9/10=18/10=9/5