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Handout 3.1 Recursive Counting
How can we interpret the notation
\(1+2+\cdots + n^2\text{?}\)
Peer instruction question 1
\begin{equation*}
\binom{n}{k} = \binom{n-1}{k-1} + \binom{n-1}{k}
\end{equation*}
Activity 3.1.1 .
Suppose that
\(f\) is a function defined on the positive integers. You know that
\(f(1) = 0\) and for all
\(n\gt 1\text{,}\) \(f(n) = 3f(n-1)+2\text{.}\) What is
\(f(3)\text{?}\)
Peer instruction question 2
Let
\(r(n)\) be the number of regions determined by
\(n\) lines in the plane drawn so that each pair intersects but no three lines intersect at a single point.
