The reason why Jayson smiled at Professor Horgan was that she gave him the next pi sequence.
What is Narration?
This refers to the storytelling that is told about a sequence of events and their order of occurence.
Hence, we can see that from the complete text, there is the narration of the interaction between Jayson and Professor Horgan and the reason for the smile was because she gave him the next pi sequence.
Read more about narrations here:
https://brainly.com/question/1934766
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