肺腺癌1a1+1a2+1a3
@贲奚4838：现有数列{an}满足:a1=1,且对任意的m,n∈N*都有:am+n=am+an+mn,则1a1+1a2+1a3+…+1a2014=( )A. -
翟委15252409659…… ∵数列{an}满足:a1=1, 且对任意的m,n∈N*都有:am+n=am+an+mn, ∴令m=1,得an+1=an+a1+n, ∴an+1-an=1+n, ∴an=a1+(a2-a1)+…+(an-an-1)=1+2+…+n= n(n+1) 2 . ∴ 1 an = 2 n(n+1) =2( 1 n ? 1 n+1 ), ∴ 1 a1 + 1 a2 + 1 a3 +…+ 1 a2014 =2(1- 1 2 + 1 2 ? 1 3 + 1 3 ? 1 4 +…+ 1 2014 ? 1 2015 )=2(1- 1 2015 )= 4028 2015 . 故选:D.
@贲奚4838：数列{an}满足a1=1且对任意的m,n∈N*都有am+n=am+an+mn,则 1 a1+ 1 a2+ 1 a3+…+ 1 a2013=( ) - 作业帮
翟委15252409659…… [选项] A. 2013 2014 B. 4026 2014 C. 2012 2013 D. 4024 2013
翟委15252409659…… ∵数列{an}满足:a1=1, 且对任意的m,n∈N*都有:am+n=am+an+mn, ∴令m=1,得an+1=an+a1+n, ∴an+1-an=1+n, ∴an=a1+(a2-a1)+…+(an-an-1)=1+2+…+n= n(n+1) 2 . ∴ 1 an = 2 n(n+1) =2( 1 n ? 1 n+1 ), ∴ 1 a1 + 1 a2 + 1 a3 +…+ 1 a2014 =2(1- 1 2 + 1 2 ? 1 3 + 1 3 ? 1 4 +…+ 1 2014 ? 1 2015 )=2(1- 1 2015 )= 4028 2015 . 故选:D.
@贲奚4838：数列{an}满足a1=1且对任意的m,n∈N*都有am+n=am+an+mn,则 1 a1+ 1 a2+ 1 a3+…+ 1 a2013=( ) - 作业帮
翟委15252409659…… [选项] A. 2013 2014 B. 4026 2014 C. 2012 2013 D. 4024 2013
