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- TL;DR Summary
- Concerns a particular inequality in demonstrating the e = lim ( 1 + 1/n)^n ...

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 2.3.15 ...

Proposition 2.3.15 and its proof read as follows:

In the above proof by Sohrab, we read the following:

" ... ... It follows that ##t_n \leq s_n## so that

##\text{ lim sup } ( t_n ) \leq e## ... ... "

Can someone please explain exactly how/why ##t_n \leq s_n \Longrightarrow \text{ lim sup } ( t_n ) \leq e## ... ... ?

Help will be 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 2.3.15 ...

Proposition 2.3.15 and its proof read as follows:

In the above proof by Sohrab, we read the following:

" ... ... It follows that ##t_n \leq s_n## so that

##\text{ lim sup } ( t_n ) \leq e## ... ... "

Can someone please explain exactly how/why ##t_n \leq s_n \Longrightarrow \text{ lim sup } ( t_n ) \leq e## ... ... ?

Help will be appreciated ... ...

Peter