Question

3. prove that \Sigma 1/ [n ln n (ln ln n)^p] converges if and only if p>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: a natural number n is prime if and only if sigma(n) =
n+1

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

How do I show whether sigma(n=1 to infinity) sqrt(n)/(1+n^2)
converges or not?

suppose sigma n=1 to infinity of square root ((a_n)^2 +
(b_n)^2)) converges. Show that both sigma a_n and sigma b_n
converge absolutely.

Prove that a sequence (un such that n>=1)
absolutely converges if the limit as n approaches infinity of
n2un=L>0

sigma(k=n)(infinity) (1/3)^k is equal to?? (non sigma notation
version, only numbers)

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?)

Given the alternating series:
sigma(2 to infinity): (-1)^n / ln n
Determine if the series converge
absolutely. (Use the fact
that: ln n <
n)
Determine if the series converge
conditionally.
(Estimate the sum of the infinite series using the
first 4 terms in the series and estimate the
error.
How many terms should we use to approximate the sum of
the infinite series in question, if we want the error to be less
than 0.5?

prove that a sequence converges if and only if all subsequences
converge to the same limit

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