The following function is defined for all
, and
is a positive integer. Prove or provide a counterexample to the following statement.
Assume exists for all
and is bounded,
for some constant for all
. Then,
Incomplete.
Counterexample. Let
. Then,
, and
for all
. From a prior counterexample (exercise 22), we know that although the sequence
converges to zero, the infinite integral
diverges.