1/2+1/6+1/12+1/20+1/30+1/42+1/56=?简便运算.
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/13 15:30:24
![1/2+1/6+1/12+1/20+1/30+1/42+1/56=?简便运算.](/uploads/image/z/66505-49-5.jpg?t=1%2F2%2B1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B1%2F42%2B1%2F56%3D%3F%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97.)
1/2+1/6+1/12+1/20+1/30+1/42+1/56=?简便运算.
1/2+1/6+1/12+1/20+1/30+1/42+1/56=?简便运算.
1/2+1/6+1/12+1/20+1/30+1/42+1/56=?简便运算.
1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8
1/2+1/6+1/12+1/20+1/30+1/42+1/56=?
因为1/n*(n+1)=1/n-1/(n+1)
suoyi
1/2+1/6+1/12+1/20+1/30+1/42+1/56=1-1/8=7/8
1/2+1/6+1/12+1/20+1/30+1/42+1/56=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)=1-1/8=7/8