a1=1,an+1=an平方+an(n∈n*)数列bn满足bn=1/1+an设tn=b1b2...bn试用an+1表示tn,并求tn最大值

a1=1,an+1=an平方+an(n∈n*)数列bn满足bn=1/1+an设tn=b1b2...bn试用an+1表示tn,并求tn最大值
a1=1,an+1=an平方+an(n∈n*)数列bn满足bn=1/1+an设tn=b1b2...bn试用an+1表示tn,并求tn最大值

a1=1,an+1=an平方+an(n∈n*)数列bn满足bn=1/1+an设tn=b1b2...bn试用an+1表示tn,并求tn最大值
a(n+1)=an²+an=an(1+an)
1+an=a(n+1)/an
bn=1/(1+an)=an/a(n+1)
b(n-1)=1/[1+a(n-1)]=a(n-1)/an
…………
b1=1/(1+a2)=a1/a2
连乘
Tn=b1b2...bn=a1/a(n+1)=1/a(n+1)
数列各项均为正.
a(n+1)/a=1+an>1 a(n+1)>an,1/a(n+1)