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I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition).
I am focused on Chapter 2: Sequences and Series of Real Numbers ... ...
I need help with an aspect of the proof of Proposition 2.3.12 ...
Proposition 2.3.12 and its proof read as follows:
View attachment 9051
In the above proof by Sohrab we read the following:
" ... ... Now if $$p \leq 1$$, then $$1 / n^p \geq 1 / n \ \forall \ n \in \mathbb{N}$$ ... "My question is ... how do we know this is true ... ?
Can someone please demonstrate how to prove that if $$p \leq 1$$, then $$1 / n^p \geq 1 / n \ \forall \ n \in \mathbb{N}$$ ...
Help will be much appreciated ...
Peter
I am focused on Chapter 2: Sequences and Series of Real Numbers ... ...
I need help with an aspect of the proof of Proposition 2.3.12 ...
Proposition 2.3.12 and its proof read as follows:
View attachment 9051
In the above proof by Sohrab we read the following:
" ... ... Now if $$p \leq 1$$, then $$1 / n^p \geq 1 / n \ \forall \ n \in \mathbb{N}$$ ... "My question is ... how do we know this is true ... ?
Can someone please demonstrate how to prove that if $$p \leq 1$$, then $$1 / n^p \geq 1 / n \ \forall \ n \in \mathbb{N}$$ ...
Help will be much appreciated ...
Peter