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设数列{bn}满足:,bn+1=bn2+bn,(1)求证:;(2)若Tn=++…+,对任意...
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设数列{b
n}满足:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAjCAYAAADmOUiuAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAFISURBVFhH7ZaBCcQgDEWdzJ1cx2UcxVFyRq21
6nmxKTQcFuQoxOvzx/xEgfBHCeeDDUjOkLeglQbrrztkKOgMKKXCkgoYRXNgNiD5wo0Ct4Is+f7g
DjqDZR6WcVwpbu4n3EFvNbzCF006CxR+a4bKqD1YbYIb3X+S2dIW9SsnIJ7iFfnmqAUwpRfvQVZA
W2jaIvXQj8ZlQEwvgh0pTu8SBE2Ag/RiVa8CUu8fxh3PbA/GxMi+elHBfrJ4NHfEPwuAg+rF8WdV
PuIHV8NUl944m/HsZhViFh9TXLrIr07yZeplA5WBNRRq4x70iXoy9bIALwWaba66XnTASDHulxxA
H7y39lss2FrF1wG7wzUFKg6w9V9ZgIOGIQhwPE2JAXRm3LlEAHatNhTK4TR0wMnUy7GZS5Mow+7Z
yeiAHArG3g3IEC9uFa/gB3OKsEFL/9SyAAAAAElFTkSuQmCC
)
,b
n+1=b
n2+b
n,
(1)求证:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGAAAAAqCAYAAABMW14yAAAAAXNSR0IArs4c6QAAAARnQU1BAACx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)
;
(2)若T
n=
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAqCAYAAABP7FAaAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAEfSURBVFhH7VZbDsQgCPRk3MnrcBmP4lFY6Pro
ptUVmrZpYxOTfogjM4Dj6IbP3YBJDwKNSOCAMNp40mcaPDnneF0JuiQXyE/QAZn1mk56B2jNWx5C
7zIYpE+/ywdFimmrMVM90Dpigh7j708010Itiiv+5T5T03M1PfX0xuFJU3mUj7mB3fMbtqYWkmwA
JKPt2WJ2bE0BjQgEFqfFh7fn776tKaDBs9HCbLo8u6DBzw6aNE1XDl7xephBhf8VR0J178mSSzWn
109gh96F2lJBkRAUntaWKd9mXbXaKjaBclCt2n06hM5mZZtAuTMRskbbqhV9RT91O3VszdArY+7h
/hjs9+QEHZxZm21T00JJbhlT2xypXqt2rbghTV8B+gHdQ9gs1L1B7QAAAABJRU5ErkJggg==
)
+
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAqCAYAAABP7FAaAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAFDSURBVFhH7VftDYQgDGUydmIdlmEURum1HIie
Am31NCaYmPij9NHXr6eBBx7zACa8CDR6sMaCjzqe5JEGB8YYfO8ETcEFcBOUkWZ5Tie9DFqLyUvo
TYOB+vT7uiAIMZsqI5UDrU9M0HP8DU5jLdSiuOOb7jNz+t+c/tV7w3nOKS3lc2rg0H9D1tRCIgPr
QSl79pgdWbOARm/BapQWOm/P32NZs4AGh0LLF9HlUAUxHz1ozmm+cnCC7aEGJf5XHBHVvZVFl2pO
r83BDr2J2qWCIngr0LS6SPE266qVVrEKFA/Vqv2lg6IuVDaKSwWKndlyHLGaC+0pj5I+7sga/pZJ
TgSt1Ok4Pmj6f7kbFCN1mol1EDE70uCvm8ss0NGwYA7MxWwIul0EAefz+T3UBd2PO8GkuqZ6pSS2
7Yf0XgdVPT0C+gFS6M6cZv9AZgAAAABJRU5ErkJggg==
)
+…+
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAqCAYAAABP7FAaAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAFDSURBVFhH7VYBDoMgDORl/Inv8BmewlO6FkHR
SbF1zplhYmIicNxdC2fghsfcgAkPAo0erLHgo04nOdPgwBiD7zdBE7kAboAesFnu6ZD3gKxlyEPk
TQcD9en0uiCgmIcqmcqB6hkD9Jx+ndlYC0tRfOOb9jM8vdbTS1dvLJ49pUv5XBrYXb8Ra5ZCogHW
gzL2vGMysWYGjd6C1SQtXLx9/u7Hmhk0OAxavoQuhyno4KMHzZ7mLQcnuD3UoKR/pRFJzV1ZtKnm
6bWayMibpJ0rKIK3gkyrY4q7qatWWsUqUJy0VK0iRKtAsTO9LR4JqrZX3Eys+cVbJrdS8rz+7tHk
//NMY4SYPA9oAUqfJDtvQVde6kmLgKmlNv2s5dsBnarZhamJRScVsyMetGb2IWm7GWnFrFxVmki/
Yd31VOsbN+9/QF82D8vkC31msQAAAABJRU5ErkJggg==
)
,对任意的正整数n,3T
n-log
2m-5>0恒成立.求m的取值范围.
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