Finding Intervals of Convergence In Exercises 49-52, find the intervals of convergence of (a). f ( x ) (b) f ' ( x ) , (c) f " ( x ) . and (d) ∫ f ( x ) d x . . (Be sure to include a check for convergence at the endpoints of the intervals.) f ( x ) = ∑ n = 1 ∞ ( − 1 ) n + 1 ( x − 1 ) n + 1 n + 1
Finding Intervals of Convergence In Exercises 49-52, find the intervals of convergence of (a). f ( x ) (b) f ' ( x ) , (c) f " ( x ) . and (d) ∫ f ( x ) d x . . (Be sure to include a check for convergence at the endpoints of the intervals.) f ( x ) = ∑ n = 1 ∞ ( − 1 ) n + 1 ( x − 1 ) n + 1 n + 1
Solution Summary: The author calculates the Interval of convergence of la, b, and c.
Finding Intervals of Convergence In Exercises 49-52, find the intervals of convergence of (a).
f
(
x
)
(b)
f
'
(
x
)
, (c)
f
"
(
x
)
. and (d)
∫
f
(
x
)
d
x
.
. (Be sure to include a check for convergence at the endpoints of the intervals.)
f
(
x
)
=
∑
n
=
1
∞
(
−
1
)
n
+
1
(
x
−
1
)
n
+
1
n
+
1
(-1)
Let g(x) = E-o
(2n):
Find the interval of convergence g.
2n
Let an=
7n + 1
(a) Determine whether (an} is convergent.
convergent
divergent
(b) Determine whether an is convergent.
n = 1
convergent
divergent
f(x) =
n2
n = 1
Find the intervals of convergence for f. (Enter your answers using interval notation.)
Find the intervals of convergence for f'.
Find the intervals of convergence for f".
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