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数列{an}的首项a1=1,前n项和为Sn,满足关系3tSn-(2t+3)Sn-1=3t(...
试题详情
数列{a
n}的首项a
1=1,前n项和为S
n,满足关系3tS
n-(2t+3)S
n-1=3t(t>0,n=2,3,4…)
(1)求证:数列{a
n}为等比数列;
(2)设数列{a
n}的公比为f(t),作数列{b
n},使b
1=1,b
n=f(
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABsAAAAqCAYAAABC8iBdAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAFESURBVFhH7VdtDoMgDOVkXGYnILsNl+EoHKVr
KygSN9qGGX9gYmIy5/N99EMHNx7uRix4OFiO4J2HmPWa6JilAM45PO8AYzIJwgLrbNV5tmT8UhUP
lpELmupsO0PSFbaBmQ6gvXuB2bVr/ok+H4b/85owl2dzPJvyFOFDimc0EO0TWIjVBIRakY9gWC2k
WAdYjh68ZYsRQzXRTwGXmFgXmoCbxvzj7Flp4ynoO7rk1TYwWtGaeUGSaseHGIwl3JORIXrbXjgC
RGYY+zaFf0ylIwmPFNoX0J4V+d6nG5mRbLXzz0kheU4T5AJspLTt96u6HYyY0sbY0/Z6/AJ6sJwh
s6cJpUaJebt6wXuXvRu8XfmoZWSjEYhLo6vHX/z0zMrnUUhbEWo6ix6sZcISytOqBjsxqV+dgj5W
o9/Hfy0848IS3PEB38uZOJ5IoncAAAAASUVORK5CYII=
)
),(n=2,3,4…),求b
n(3)求T
n=(b
1b
2-b
2b
3)+(b
3b
4-b
4b
5)+…+(b
2n-1b
2n-b
2nb
2n+1)的值.
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