March 11th, 2019, 06:34 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 511 Thanks: 79  Infinite product
How to show whether the infinite product converges ? $\displaystyle p=\prod_{n=1}^{\infty } \prod_{m=1}^{\infty } \frac{n}{10^{m}} \; \; $ , $\displaystyle n,m \in \mathbb{N}$ . Is p the product of all numbers in interval $\displaystyle (0,1)$ ? 
March 11th, 2019, 08:48 AM  #2 
Senior Member Joined: Dec 2015 From: somewhere Posts: 511 Thanks: 79 
I posted it wrong , the variable n is from 1 to m .

March 11th, 2019, 09:59 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,632 Thanks: 2080 
Are you sure it isn't still wrong?

March 11th, 2019, 10:04 AM  #4 
Senior Member Joined: Dec 2015 From: somewhere Posts: 511 Thanks: 79 
No delete the thread ,I will open another thread if needed . Free to delete or close the thread . 

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