问题
填空题
已知等比数列{an}中,a1=3,a4=81,若数列{bn}满足bn=log3an,则数列{
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答案
q3=
=27,求得q=3a4 a1
∴an=3×3n-1=3n,
∴bn=log3an=n,
=1 bnbn+1
=1 n(n+1)
-1 n 1 n+1
∴Sn=1-
+1 2
-1 2
+…+1 3
-1 n
=1-1 n+1
=1 n+1 n n+1
故答案为:n n+1