1.3, due on September 10
Difficult:
I had a hard time understanding the difference in indexing in Threorem 1.3.10 (The Fundamental Theorem of Finite Calculus) -- why is b-1 used in (1.6) and n-1 used in (1.7)? Also, the whole idea of the difference operator and finite calculus is pretty new and it will take some time to develop the intuition for it.
Reflective:
The proof of the geometric series formula using the FTFC was super cool. I liked the trick where they multiplied the sum by (r - 1) initially and then distributed it, which allowed them to work with function that had the difference operator applied to it, then use the FTFC to further simplify.
I had a hard time understanding the difference in indexing in Threorem 1.3.10 (The Fundamental Theorem of Finite Calculus) -- why is b-1 used in (1.6) and n-1 used in (1.7)? Also, the whole idea of the difference operator and finite calculus is pretty new and it will take some time to develop the intuition for it.
Reflective:
The proof of the geometric series formula using the FTFC was super cool. I liked the trick where they multiplied the sum by (r - 1) initially and then distributed it, which allowed them to work with function that had the difference operator applied to it, then use the FTFC to further simplify.
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