Review

Given a sequence, say,

\( a_n = 2n\)     (\(n = 0\), \(1\), \(2\), \(...\))

We can create a new sequence \(s_n\) of the sum of the first terms of the sequence above:

\(s_0 = a_0\)
\(s_1 = a_0 + a_1\)
\(s_2 = a_0 + a_1 + a_2\)
    \(\vdots\)

Since \(a_0 = 0\), \(a_1 = 2\), and \(a_2 = 4\), this means \(s_n\) will be a sequence beginning with terms: \(0\), \(2\), \(6\), \(...\)

An infinite sequence of partial sums like this is called a series and would be written (with \(n\), \(i\), or \(k\), etc.) like:

\(\sum\limits_{n=0}^{\infty} 2n\)

How to Play

When you see the series formula,

1. check its starting index (usually \(0\) or \(1\)), then
2. start entering the first partial sums as quickly as you can.

Enter as many partial sums as you can until the timer runs out for that series. You keep playing and racking up points until you:

• enter an incorrect answer, or
• don't enter at least 3 partial sums for a series.