Sequences and Series, Increasing/Decreasing
Increasing/Decreasing
f() (a real valued function) is monotonically increasing if,
for every x1 < x2, f(x1) ≤ f(x2).
f is strictly increasing if,
for every x1 < x2, f(x1) < f(x2).
Similarly, f can be monotonically or strictly decreasing.
The same definitions apply to sequences;
just make sure x1
and x2
are integers.
A series of positive terms produces a strictly increasing sequence of partial sums.
A series of nonnegative terms produces a monotonically increasing sequence of partial sums.