Outline: See Feb. 28, 2012, class notes for details.
Sigma/summation notation: delimited form
The sum Sn of n terms of a sequence may be formed recursively,
so we may generate Sn by a recurrence relation.
General sigma/summation notation
- Sum of (ak+bk)
- Sum of c ak
- Sum of ak for k in the union of
disjoint index sets
- The index is a "dummy variable."
- Simple "shift" substitution in a sum
- Parallels with integral calculus
- See the chart with integral calculus
and summation calculus is parallel columns.
- The sum of f(k) for a < k < b
behaves analogously to the integral of
f(x) for a < x < b or
a < x < b.
- In-class exercises