1.观察下面的算式:6☆2=6+7=13 2☆3=2+3+4=9 5☆4=5+6+7+8=26 根据上面式子所表示的运算,求7☆5.
问题描述:
1.观察下面的算式:6☆2=6+7=13 2☆3=2+3+4=9 5☆4=5+6+7+8=26 根据上面式子所表示的运算,求7☆5.
2.(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×……×(1+1/99)×(1-1/99)
答
1) 7☆5=7+8+9+10+11=45
☆表示从7开始,连续加5个数.
2) (1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×……×(1+1/99)×(1-1/99)
=(3/2) × (1/2) × (4/3) × (2/3) × (5/4) × (3/4) ×.×(99/98) × (97/98) × (100/99) × (98/99)
=[(3/2) × (4/3)× (5/4) ×.×(99/98) × (100/99)]× [(1/2) × (2/3) × (3/4) ×.×(97/98) × (98/99)]
=[(1/2) × (1/1)× (1/1) ×.×(1/1) × (100/1)]× [(1/1) × (1/1) × (1/1) ×.×(1/1) × (1/99)]
=[100/2] × [1/99]
=50/99
把所有(1+1/n)的放一起,把所有(1-1/n)的放一起第一题有什么规律么?