若Sn=
|
∵Sn=
+1 2
+2 3
+1 22
+…+2 32
+1 2n 2 3n
=(
+1 2
+…+1 22
)+…+2(1 2n
+1 3
+••+1 32
) ))1 3n
=
+2•
[1-(1 2
)n]1 2 1- 1 2
[1-(1 3
)n]1 3 1- 1 3
=2-(
)n-(1 2
)n1 3
则
Sn=lim n→∞
(2-lim n→∞
-1 2n
)=21 3n
故答案为:2
若Sn=
|
∵Sn=
+1 2
+2 3
+1 22
+…+2 32
+1 2n 2 3n
=(
+1 2
+…+1 22
)+…+2(1 2n
+1 3
+••+1 32
) ))1 3n
=
+2•
[1-(1 2
)n]1 2 1- 1 2
[1-(1 3
)n]1 3 1- 1 3
=2-(
)n-(1 2
)n1 3
则
Sn=lim n→∞
(2-lim n→∞
-1 2n
)=21 3n
故答案为:2