Indeterminate form, Powers
:
Geometric Series
:
*r is the ratio
Is convergent if |r|
1
between terms
Is divergent if |r|
1
Integral Text:
Suppose f is a continuous, positive, decreasing function on [1,
) and let A
= f(n). Then the
series
A
is convergent if and only if the improper integral
f(x) dx is convergent. In other words:
1.
f(x) dx is convergent, then
A
is convergent.
2.
f(x) dx is divergent, then
A
is divergent
P-series test
:
The P-series
is convergent if p
1 and divergent if p
1.
Comparison Test
: Suppose that
A
and
B
are series with positive terms.
1. If
B
is convergent and A
B
for all n, the
A
is also convergent.
2. If
B
is divergent and A
B
for all n, then
A
is also divergent.
Limit Comparison Test
: Suppose that