Q1270 (Q1270): Difference between revisions

@@ Property / relevant answers / Property / relevant answers @@
-https://math.stackexchange.com/a/3124622
+3124622
-Defining formula:  $0<a_{n}=\prod _{k=1}^{n}\left(1-{\frac {1}{\sqrt {k+1}}}\right)<\prod _{k=1}^{n}\left(1-{\frac {1}{k+1}}\right)={\frac {1}{n+1}}\rightarrow 0$ 
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}\rightarrow0
@@ Property / relevant answers / Property / relevant answers @@
-https://math.stackexchange.com/a/381303
-relevant answers: \lim_{n\to\infty}\log a_n=\sum_{k=1}^\infty \log  \left(1-\dfrac{1}{\sqrt{k+1}}\right)

Latest revision as of 13:27, 20 May 2020