Finding the Interval of Convergence In Exercises 41-44, find the interval of convergence or the power series, where c > 0 and k is a positive integer. (Be sure to include a check for convergence at the endpoints of the interval.) ∑ n = 1 ∞ k ( k + 1 ) ( k + 2 ) ⋯ ( k + n − 1 ) x n n !
Finding the Interval of Convergence In Exercises 41-44, find the interval of convergence or the power series, where c > 0 and k is a positive integer. (Be sure to include a check for convergence at the endpoints of the interval.) ∑ n = 1 ∞ k ( k + 1 ) ( k + 2 ) ⋯ ( k + n − 1 ) x n n !
Solution Summary: The author explains how to determine the interval of convergence of the power series.
Finding the Interval of Convergence In Exercises 41-44, find the interval of convergence or the power series, where c > 0 and k is a positive integer. (Be sure to include a check for convergence at the endpoints of the interval.)
∑
n
=
1
∞
k
(
k
+
1
)
(
k
+
2
)
⋯
(
k
+
n
−
1
)
x
n
n
!
Using the root test, the series E(-1)"(1-2)
n2
(A) The root test fails.
(B) Converges conditionally
(C) Diverges
(D) Converges absolutely
(E) None of the above.
A O
B O
.C
D O
E O
Real Analysis
I must determine if the two series below are divergent, conditionally convergent or absolutely convergent. Further I must prove this. In other words, if I use one of the tests, like the comparison test, I must fully explain why this applies.
a) 1-(1/1!)+(1/2!)-(1/3!) + . . .
b) (1/2) -(2/3) +(3/4) -(4/5) + . . .
Thank you.
Geometric series In Section 8.3, we established that the geo-
metric series Ert converges provided |r| < 1. Notice that if
-1
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