Question

已知数列an,满足an=9^n (n 1)/10^n,试问an有没有最大项?若有求出最大值.是9的n次方再乘以.

Answer 1

an=9^n*[(n+1)]/10^n

=(9/10)^n*[(n+1)]

则:a(n+1)/an

={(9/10)^(n+1)*[(n+2)]}/{(9/10)^n*[(n+1)]}

=(9/10)*[(n+2)/(n+1)]

=(9/10)*[1+1/(n+1)]

令a(n+1)/an≥1,得1≤n≤8,

令a(n+1)/an≤1,得n≥8,

故当n=8时,a8=a9

na(n+1) 数列递减

所以最大值为a8和a9

a8=a9=9^9/10^8.