Question

Determine whether each of the following series converges or not.
(Name the test you use. You do not have to evaluate the sums of
these series). **Please write as large and neatly as possible
in your answer for ease of reading, demonstrating all steps. Thank
you.**

a) Sum infinity n = 1 of square root n/n^3+1

b) Sum infinity n = 2 of 1/nln(n)

Answer #1

Determine whether each of the following series converges or not.
(Name the test you use. You do not have to evaluate the sums of
these series). Please write as big and neatly as possible
in your answer, demonstrating all steps.
a) Sum infinity n = 1 of square root n/n^3+1
b) Sum infinity n = 2 of 1/nln(n)

Use the RATIO test to determine whether the series is convergent
or divergent.
a) sigma from n=1 to infinity of (1/n!)
b) sigma from n=1 to infinity of (2n)!/(3n)
Use the ROOT test to determine whether the series converges or
diverges.
a) sigma from n=1 to infinity of
(tan-1(n))-n
b) sigma from n=1 to infinity of ((-2n)/(n+1))5n
For each series, use and state any appropriate tests to decide
if it converges or diverges. Be sure to verify all necessary...

Use the ratio test to determine whether∑n=12∞n2+55n
converges or diverges.
(a) Find the ratio of successive terms. Write your
answer as a fully simplified fraction. For n≥12,
limn→∞∣∣∣an+1an∣∣∣=limn→∞
(b) Evaluate the limit in the previous part. Enter ∞
as infinity and −∞ as -infinity. If the limit does
not exist, enter DNE.
limn→∞∣∣∣an+1an∣∣∣ =
(c) By the ratio test, does the series converge,
diverge, or is the test inconclusive?

Determine if each of the following series converges or diverges
showing all the work including all the tests used. Find the sum if
the series converges.
a. Σ (n=1 to infinity) (3^n+1/ 7^n)
b. Σ (n=0 to infinity) e^n/e^n + n

Prove whether or not the series converges
a) sum of ( 6n2 + 89n +73)/(n4 - 213n)
from 1 to infinity
b) sum of 1/(n3 +2) from 0 to infinity
c) sum of n1/n from 1 to infinity
d) sum of (-1)n /ln(n) from 2 to infinity (why we
start with 2 instead of 1?)

Determine if the series converges conditionally, converges
absolutely, or diverges.
/sum(n=1 to infinity) ((-1)^n(2n^2))/(n^2+4)
/sum(n=1 to infinity) sin(4n)/4^n

State whether the given series converges or diverges, and
why.
#21 sum 1/n^5, n=1 to infinity
#22 sum 1/5^n, n=0 to infinity
#23 sum 6^n / 5^n, n=0 to infinity
#24 sum n^-4, n=1 to infinity
#25 sum sqrt(n), n=1 to infinity

Determine if the series converges or diverges. Justify your
answer by stating the test used and the conditions of the test.
\sum _{n=0}^{\infty } [100+\sqrt{n}]/[4n^2-6n+1]

Determine if each of the following series converges or diverges
showing all the work including all the tests used.
a. Σ (n=2 to infinity) 3^n+2/ln n
b. Σ (n=1 to infinity) (-3)^n/n^3 2^n

Determine whether the series
∞
∑
n=1
(e^n+1+ (−1)^n+1)/(π^n)
converges or diverges. If it is convergent, find its
sum.

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