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正数数列{an}的前n项和Sn,满足4Sn=(an+1)2,试求:(1)数列{an}的通项...
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正数数列{a
n}的前n项和S
n,满足4S
n=(a
n+1)
2,试求:
(1)数列{a
n}的通项公式;
(2)设b
n=
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAqCAYAAADBNhlmAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAFRSURBVFhH7ZdRksIgDEBzMi6zJ2C8DZfhKBwl
JqHuUBcbDdmRj7wZHK2meZQ0UsDNCcFV/ARbwQQJSzs+O+EjWDMCAI1dBYWKOQSXCMFVQnCVnQWl
SXMf7CPX47gDjlfwfwjBVfYXfBT2jkME5XVjQnCVEFwlBFcZBHk3wv2HdiSV//wzHdGwxHxGFzw9
MjYsiZJqWxJLjAES7Ccfz10zYLrc2FlibIA8055mzsmVjaclxgjwzMdcrSSEVCjlaywxVk6CkoiK
XlsqS8w7zMqkL7Hcif1L/pGa0BLzC5VDGcuj82qiX+iDc0GGJT8UPPqc1Nf4/gotxlOwNWy0nIlO
WBI1Yel9SjOexvzgjfskyz6P4W4zXMGjcCmRxP1pL3OuY9yXONEd24M4se6nxXgKjrN/Z3kZNcZR
8DR7TvxUMzMsMQzLPepylFRr8NuE4BqId7Ykg+evga0PAAAAAElFTkSuQmCC
)
,数列的前n项的和为B
n,求证:B
n<
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACeSURBVDhP3ZLREQMhCESpjJ5oh2YohVIIoGcg
Xi4/l3xkZ/BG54l7q2AfdCegbAhorHM+NQAhAwCvd0BKjP4cyJAih1EkuZoqHc71C+AwdlYJ5Hih
u4D1YLyQrYYJmeKKLuJ2qEQJKtJ2KGPrsnuI42qH+V0Surqs5meoAGqM5Da7FiC0P5ZQAuG8dXaj
xxzCVL2gUc+jtr941dcBswdgFekEiSLONQAAAABJRU5ErkJggg==
)
;
(3)设c
n=a
n•(
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAjCAYAAACpZEt+AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACVSURBVDhP3ZPREYQwCESpjJ7SDs2kFEpZCUQH
uej9ePfhm8EZ9WnWVQlfeFJQARNDdO5PQugNRGRzJTgd7eWClzR6iGndjzrpDmv+IezBVuOCb294
SshF5ZYME6xiFkTDo+7apOo8GfR2V/X4Nj+XCMaVFxkSMyynd34WDBUGHaEXQs1RBIVwfYrjr4op
GRdLFH4uABs3bOp5PAM6+AAAAABJRU5ErkJggg==
)
)
n,求数列{c
n}的前n项和T
n.
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