Q1270 (Q1270): Difference between revisions

@@ Property / relevant answers / Property / relevant answers @@
-https://math.stackexchange.com/a/3124622
+3124622
@@ Property / relevant answers: 3124622 / qualifier @@
+our score: 2Amount 2
Unit 1
 Amount
 Unit

Revision as of 16:14, 14 May 2020

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English	No label defined	No description defined

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A.60

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0<a_{n}=\prod _{k=1}^{n}\left(1-{\frac {1}{\sqrt {k+1}}}\right)<\prod _{k=1}^{n}\left(1-{\frac {1}{k+1}}\right)={\frac {1}{n+1}}\rightarrow 0

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\lim _{n\to \infty }\log a_{n}=\sum _{k=1}^{\infty }\log \left(1-{\dfrac {1}{\sqrt {k+1}}}\right)

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