1+3又1/6+5又1/12+7又1/20+9又1/30+11又1/42+13又1/56+15又1/72+17又1/90+19又1/101
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 07:18:21
![1+3又1/6+5又1/12+7又1/20+9又1/30+11又1/42+13又1/56+15又1/72+17又1/90+19又1/101](/uploads/image/z/4872-48-2.jpg?t=1%2B3%E5%8F%881%2F6%2B5%E5%8F%881%2F12%2B7%E5%8F%881%2F20%2B9%E5%8F%881%2F30%2B11%E5%8F%881%2F42%2B13%E5%8F%881%2F56%2B15%E5%8F%881%2F72%2B17%E5%8F%881%2F90%2B19%E5%8F%881%2F101)
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1+3又1/6+5又1/12+7又1/20+9又1/30+11又1/42+13又1/56+15又1/72+17又1/90+19又1/101
1+3又1/6+5又1/12+7又1/20+9又1/30+11又1/42+13又1/56+15又1/72+17又1/90+19又1/101
1+3又1/6+5又1/12+7又1/20+9又1/30+11又1/42+13又1/56+15又1/72+17又1/90+19又1/101
最后一个数字如果是19又1/110 就可以按下面的做法.
思路:1/6=1/2-1/3 、1/12=1/3-1/4 、…………
1+3又1/6+5又1/12+7又1/20+9又1/30+11又1/42+13又1/56+15又1/72+17又1/90+19又1/110
=(1+3+5+7+9+11+13+15+17+19)+(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110)
=20×5+(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11)
=100+(1/2-1/11)
=100+9/22
=100又9/22