Question

已知数列an满足a1＝1/5,且当n>=2,n属于正整数时,有(a(n-1))/(an)=(2a(n-1)+1）/(1-

Answer 1

(a(n-1))/(an)=(2a(n-1)+1）/(1-2an)

=>a(n-1)*(1-2an)=an*(2a(n-1)+1)

=>a(n-1)-2ana(n-1)=2ana(n-1)+an

=>a(n-1)-an=4ana(n-1)

=>1/an-1/a(n-1)=4

设bn=1/an

=>bn-b(n-1)=4,且b1=1/a1=5

=>bn=5+4(n-1)=4n+1

=>an=1/bn=1/(4n+1)

=>a1a2=1/5*1/9=1/45=1/(4*11+1

=>n=11

=>第十一项