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 = 0 ∞ ( − 1 ) n + 1 ( x − c ) n n c n
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 = 0 ∞ ( − 1 ) n + 1 ( x − c ) n n c n
Solution Summary: The author calculates the interval of convergence of the power series (0,2c).
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.)
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.
(a) Find the series' radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally.
nx"
n=0 11"
(a) The radius of convergence is.
(Simplify your answer.)
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