简便运算:1/2+(-1/6)+(-1/12)+(-1/20)+(-1/30)+(-1/42)=?9月22日21:00前,追加50分,绝不违约!
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/29 07:14:48
简便运算:1/2+(-1/6)+(-1/12)+(-1/20)+(-1/30)+(-1/42)=?9月22日21:00前,追加50分,绝不违约!
简便运算:1/2+(-1/6)+(-1/12)+(-1/20)+(-1/30)+(-1/42)=?
9月22日21:00前,追加50分,绝不违约!
简便运算:1/2+(-1/6)+(-1/12)+(-1/20)+(-1/30)+(-1/42)=?9月22日21:00前,追加50分,绝不违约!
1/2+(-1/6)+(-1/12)+(-1/20)+(-1/30)+(-1/42)
=1/2+(1/3-1/2)+(1/4-1/3)+(1/5-1/4)+(1/6-1/5)+(1/7-1/6)
=1/2+1/3-1/2+1/4-1/3+1/5-1/4+1/6-1/5+1/7-1/6
=1/7
1/2+ 1/6+ 1/12+ 1/20+1/30 +1/42
=1/2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
1/2+(-1/6)+(-1/12)+(-1/20)+(-1/30)+(-1/42)
=1/2+[-1/(2*3)]+[-1/(3*4)]+[-1/(4*5)]+[-1/(5*6)]+[-1/(6*7)]
注:1/[N(N+1)]=1/N-1(N+1)
=1/2-1/2+1/3.........-1/6+1/7
=1/7
1/2+(-1/6)+(-1/12)+(-1/20)+(-1/30)+(-1/42)=1/2-1/(2*3)-1/(3*4)-1/(4*5)-1/(5*6)-1/(6*7)=1/2-(1/2-1/3)-(1/3-1/4)....(1/6-1/7)=1/2-1/2+1/3-1/3....+1/6-1/6+1/7=1/7
原式=1/2-1/6-1/12-1/20-2/30-1/42
=1/2-(1/2*1/3)-(1/3*1/4)-(1/4*1/5)-(1/5*1/6)-(1/6*1/7)
=1/2-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)-(1/6-1/7)
=1/2-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6-1/6+1/7
=1/7