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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 the proof of Proposition 2.3.22 ...

Proposition 2.3.12 reads as follows:

View attachment 9054Can someone please demonstrate (formally and rigorously) how Proposition 2.322 is ( ... as Sohrab claims but does not show ... ) an immediate consequence of Cauchy's Criterion and the Triangle Inequality ...

Help will be appreciated ...

Peter

I am focused on Chapter 2: Sequences and Series of Real Numbers ... ...

I need help with the proof of Proposition 2.3.22 ...

Proposition 2.3.12 reads as follows:

View attachment 9054Can someone please demonstrate (formally and rigorously) how Proposition 2.322 is ( ... as Sohrab claims but does not show ... ) an immediate consequence of Cauchy's Criterion and the Triangle Inequality ...

Help will be appreciated ...

Peter