Question

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

Answer #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 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

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 the series converges or diverges (show your
work):
n! / nn

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

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 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)

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)

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...

Determine whether the following series converges or
diverges:∞∑n=1 ln(1 +1/n).

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