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
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![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](/uploads/image/z/5563052-44-2.jpg?t=a1%3D1%2Can%2B1%3Dan%E5%B9%B3%E6%96%B9%2Ban%28n%E2%88%88n%2A%29%E6%95%B0%E5%88%97bn%E6%BB%A1%E8%B6%B3bn%3D1%2F1%2Ban%E8%AE%BEtn%3Db1b2...bn%E8%AF%95%E7%94%A8an%2B1%E8%A1%A8%E7%A4%BAtn%2C%E5%B9%B6%E6%B1%82tn%E6%9C%80%E5%A4%A7%E5%80%BC)
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)