Question

Prove whether or not the series converges

a) sum of ( 6n^{2} + 89n +73)/(n^{4} - 213n)
from 1 to infinity

b) sum of 1/(n^{3} +2) from 0 to infinity

c) sum of n^{1/n} from 1 to infinity

d) sum of (-1)^{n} /ln(n) from 2 to infinity (why we
start with 2 instead of 1?)

Answer #1

prove whether or not the series converges: a) sum of 1/n(sqr(n))
b) sum of 5 ln(n)/n2 c) sum of (-1)n
/n1/n

prove whether the following series converge absolutely, converge
conditionally or diverge give limit
a) sum of (-5)n /n! from 0 to infinity
b) sum of 1/nn from 0 to infinity
c) sum of (-1)n /(1 + 1/n) from 0 to infinity
d) sum of 1/5n from 0 to infinity

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

Show that the series sum(an) from n=1 to infinity
where each an >= 0 converges if and only if for every
epsilon>0 there is an integer N such that | sum(ak )
from k=N to infinity | < epsilon

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 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)

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

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

Consider the following series. ∞ 1 n4 n = 1 (a) Use the sum of
the first 10 terms to estimate the sum of the given series. (Round
the answer to six decimal places.) s10 = 0.082036 Incorrect: Your
answer is incorrect. (b) Improve this estimate using the following
inequalities with n = 10. (Round your answers to six decimal
places.) sn + ∞ f(x) dx n + 1 ≤ s ≤ sn + ∞ f(x) dx n ≤ s...

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