Question

正项等差数列an,a5=8,a4*a6=60,求an和sn,设数列bn满足bn=1/sn,求Tn

Answer 1

a4+a6=2a5=16,a4a6=60,解得a4=6,a6=10,2d=a6-a4=4,d=2,an=a4+(n-4)x2=2n-2.

sn=n(n-1)/2*2=n(n-1)

1/sn=1/n(n-1)=1/(n-1)-1/n,n>=2,

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