A recipe calls for 1 3/4 cups of flour, 1 1/4 cup of white sugar, 1/3 cup of milk, 1/2 cup of walnuts, and 1/2 cup of butter. Th
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You can try to show this by induction:
• According to the given closed form, we have , which agrees with the initial value <em>S</em>₁ = 1.
• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume
and
We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or
From the given recurrence, we know
so that
which is what we needed. QED
bear in mind that the continuously compounding interest is just that, a daily compounding cycle, taking a year as 365days.