1/1*2+1/2*3+1/3*4+...+1/n(n+1)化简

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/27 14:36:11
1/1*2+1/2*3+1/3*4+...+1/n(n+1)化简
x)372672Z&zzz@VFӞi5$PΆjfjiI#Mm0 b`&Xm l C2u 5 =<;lbHUi:Ttͺg>߸u/x/7>բ O?}]xCQ2  Y0^y

1/1*2+1/2*3+1/3*4+...+1/n(n+1)化简
1/1*2+1/2*3+1/3*4+...+1/n(n+1)化简

1/1*2+1/2*3+1/3*4+...+1/n(n+1)化简
1/1*2+1/2*3+1/3*4+...+1/n(n+1)
=(1/1)-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/n)-[1/(n+1)]
=1-1/(n+1)
=(n+1-1)/(n+1)
=n/(n+1).

1/1*2+1/2*3+1/3*4+...+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)

1/1*2+1/2*3+1/3*4+...+1/n(n+1)=1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)=1-1/(n+1)
这类问题很常见的- -!

原式=(1/1-1/2)+(1/2-1/3)+……+1/n-1/(n+1)
=1-1/(n+1)