Tests for divergence of convergence
4)
a) Use the ratio test to deteremine whether the series converges
or diverges
infinite sum (4^n)/(n!)
n = 1
b) Use the root test to determine whether the series converges
or diverges
infinite sum ((2n + 1)/7n + 4) ^ 2n
n = 1
stuck on this hw question !
find the radius of convergence and interval of convergence of
the series ∑ n=1 ~ ∞ (3^n)((x+4)^n) / √n
Please solve this problem with detailed process of solving.
I can't understand why the answer is [-13/3, -11/3)
I thought that the answer was (-13/3, -11/3].
Can you explain why that is the answer?
Find the radius of convergence, R, of the series. Find
the interval, I, of convergence of the series. (Enter your
answer using interval notation
∞
(−1)n
(x −
4)n
3n +
1
n = 0
∞
(x −
4)n
n7 + 1
n = 0
∞
7n (x +
5)n
n
n = 1
∞
(x −
13)n
nn
n = 1
∞
4nxn
n2
n = 1
Use the Cauchy Criterion to prove the Bolzano–Weierstrass
Theorem, and find the point in the argument where the Archimedean
Property is implictly required. This establishes the final link in
the equivalence of the five characterizations of completeness
discussed at the end of Section 2.6.
Use the Cauchy Criterion to prove the Bolzano–Weierstrass
Theorem, and find the point in the argument where the Archimedean
Property is implictly required. This establishes the final link in
the equivalence of the five characterizations of completeness
discussed at the end of Section 2.6.