MAT 266 - Test 1 Review Question and answer verified to pass 2025/2026

MAT 266 Calculus 2
EXAM 3
trigonometric substitutions

series test for di- vergence




3. geometric
series and its 9.
sum


4. The Ratio Test



5. The Power
Series Case I

6. The Power
Series Case II

7. The Power
Series Case III


8. difference be-
tween a
geomet- ric
series and a
mathematical
se- ries




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10

, MAT 266 Calculus 2
EXAM 3
ratio of each term to its predecessor is a constant. For example,
1, 2, 4, 8, 16...
is a geometric series with ratio 2.


The series converges for all
x. In this case the radius of
convergence is R = , and
the interval of
convergence is I = (−,)

There is a real number R >
0 such that the series
converges when |x - a| < R
and diverges when |x − a|
> R. R is the radius of
convergence.

The series converges only at x
= a. In this case the radius of
convergence is R = 0, and the
interval of convergence
consists of a single point: I
= {a}

In an arithmetic series, each
value in the series ditters
from its predecessor by the
same amount. For
example,
1, 4, 7, 10, 13...
is an arithmetic series with
ditterence 3.
In a geometric series, the
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10