(n+2)(10/11)^n+1-(n+1)(10/11)^n 怎么解

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(n+2)(10/11)^n+1-(n+1)(10/11)^n怎么解(n+2)(10/11)^n+1-(n+1)(10/11)^n怎么解(n+2)(10/11)^n+1-(n+1)(10/11)^n怎

(n+2)(10/11)^n+1-(n+1)(10/11)^n 怎么解
(n+2)(10/11)^n+1-(n+1)(10/11)^n 怎么解

(n+2)(10/11)^n+1-(n+1)(10/11)^n 怎么解
设第n项为An ,
An=(n+1)(n+2)/2
=1/2N^2+3/2N+1
因为1^2+2^2+3^2+……+N^2=N(N+1)(2N+1)/6
1+2+3+……+N=N(N+1)2
1+1+1+……+1(共N个)=N
所以3+6+10+15+……+(n+1)(n+2)/2
=A1+A2+A3+……An
=1/2*N(N+1)(2N+1)/6+3/2*N(N+1)2+N
=1/6N^3+N^2+11/6N