奥数六年级1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/18 13:21:10
奥数六年级1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+
奥数六年级1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+
奥数六年级1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+
第一项化为:2/(2*3)
第二项化为:2/3*4
第三项化为:2/4*5
.
98项化为:1/99/(3/2*4/3*5/4*6/5.100/99)=1/99/(1/2*100/1)=2/(99*100)
第N项 1/(n+1)/(1/2*(n+2)/1)=2/[(n+2)*(n+1)]
合并同类项得:N项和为:2【1/2*3+1/3*4+.1/[(n+2)*(n+1)] =2【1/2-1/3+1/3-1/4+1/4-1/5+.1/(n+1)-1/(n+2)]=2[1/2-1/(n+2)]=n/(n+2)
第一项:1/2/(1+1/2)=1/2/(3/2)=2/(2*3)=2/2-2/3
第二项:1/3/(1+1/2)(1+1/3)=1/3/((3/2)*(4/3))=1/3/(4/2)=2/(3*4)=2/3-2/4
可以推测出:1/4/(1+1/2)(1+1/3)(1+1/4)=2/4-2/5
所以,原式=2/2-2/3+2/3-2/4+2/4-2/5.......-2/100
=1-1/50
=49/50
怪怪的题