Q1270 (Q1270): Difference between revisions

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@@ Property / relevant answers: 3124622 / qualifier @@
-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: 381303 / qualifier @@
-Defining formula:  $\lim _{n\to \infty }\log a_{n}=\sum _{k=1}^{\infty }\log \left(1-{\dfrac {1}{\sqrt {k+1}}}\right)$ 
\lim_{n\to\infty}\log a_n=\sum_{k=1}^\infty \log  \left(1-\dfrac{1}{\sqrt{k+1}}\right)
@@ Property / relevant answers: 381303 / qualifier @@
-our score: 1Amount 1
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