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I am reading "Introduction to Real Analysis" (Fourth Edition) b Robert G Bartle and Donald R Sherbert ...
I am focused on Chapter 2: Sequences and Series ...
I need help in fully understanding Example 3.4.3 (b) ...
Example 3.4.3 (b) ... reads as follows:
In the above text from Bartle and Sherbert we read the following:
" ... ... Note that if ##z_n := c^{ \frac{1}{n} }## then ##z_n \gt 1## and ##z_{ n+1 } \lt z_n## for all ##n \in \mathbb{N}##. (Why?) ... "Can someone help me to show rigorously that ##z_n \gt 1## and ##z_{ n+1 } \lt z_n## for all ##n \in \mathbb{N}## ... ... ?Hope that someone can help ...
Peter
I am focused on Chapter 2: Sequences and Series ...
I need help in fully understanding Example 3.4.3 (b) ...
Example 3.4.3 (b) ... reads as follows:
In the above text from Bartle and Sherbert we read the following:
" ... ... Note that if ##z_n := c^{ \frac{1}{n} }## then ##z_n \gt 1## and ##z_{ n+1 } \lt z_n## for all ##n \in \mathbb{N}##. (Why?) ... "Can someone help me to show rigorously that ##z_n \gt 1## and ##z_{ n+1 } \lt z_n## for all ##n \in \mathbb{N}## ... ... ?Hope that someone can help ...
Peter