Question

Without changing their meanings, convert each of the following sentences into a sentence having the form "If \(P\), then \(Q .\) " A series converges whenever it converges absolutely.

Short answer

The sentence 'A series converges whenever it converges absolutely' can be restated as: 'If a series converges absolutely, then the series converges'.

Step-by-step solution

Identify P and Q

The given sentence 'A series converges whenever it converges absolutely'. 'if' is equivalent to 'whenever' in creating conditions, so we can replace 'whenever' with 'if'. The part of the sentence coming after 'whenever' becomes the condition P ('it converges absolutely'). The part before this phrase then is the consequence Q ('A series converges').

Formulate The Sentence

Now that we identified the condition (P) and the consequence (Q), we can form the new sentence: 'If a series converges absolutely, then the series converges'.