Finding the Interval of Convergence In Exercises 41–44, find the interval of convergence of 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 ∞ n ! ( x − c ) n 1 ⋅ 3 ⋅ 5... ( 2 n − 1 )
Finding the Interval of Convergence In Exercises 41–44, find the interval of convergence of 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 ∞ n ! ( x − c ) n 1 ⋅ 3 ⋅ 5... ( 2 n − 1 )
Solution Summary: The author explains that the interval of convergence of the power series is underset_(-2+c,2 +c).
Finding the Interval of Convergence In Exercises 41–44, find the interval of convergence of 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
∞
n
!
(
x
−
c
)
n
1
⋅
3
⋅
5...
(
2
n
−
1
)
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.
Real Analysis
Prove that the series (a1-a2)+(a2-a3)+(a3-a4)+ . . . converges if and only if the sequence {an}n=1 to infinity converges.
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