1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45这个数学题?算
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 18:26:28
![1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45这个数学题?算](/uploads/image/z/17049-57-9.jpg?t=1%EF%BC%8F3%2B1%EF%BC%8F6%2B1%EF%BC%8F10%2B1%EF%BC%8F15%2B1%EF%BC%8F21%2B1%EF%BC%8F28%2B1%EF%BC%8F36%2B1%EF%BC%8F45%E8%BF%99%E4%B8%AA%E6%95%B0%E5%AD%A6%E9%A2%98%3F%E7%AE%97)
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45这个数学题?算
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45这个数学题?算
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45这个数学题?算
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45
=2*(1/6+1/12+1/20+1/30+1/42+...+1/90)
=2*(1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+...+1/9*10)
=2*(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+...+1/9-1/10)
=2*(1/2-1/10)
=2*2/5
=4/5
答案4/5。用计算器算de。
1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45
=(1/3+1/6)+(1/10+1/15)+(1/21+1/28)+(1/36+1/45)
=1/3(1+1/2)+1/5(1/2+1/3)+1/7(1/3+1/4)+1/9(1/4+1/5)
=1/3*3/2+1/5*5/6+1/7*7/12+1/9*9/20
=1/2+1/6+1/12+1/20
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)
=1-1/5
=4/5