Question

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

Answer #1

**Please comment if you have any doubt.**

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

Determine where series converges or diverges:
∑(-1)n(n!)2/(2n)!

Determine whether the limit converges or diverges, if it
converges, find the limit.
an = (1+(4/n))^n

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 sequence a_n = (3^n + 4^n)^(1/n) diverges
or converges

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

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 the sequence converges or diverges.
a_n=(-1)^n n+7/n^2+2

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 sequence converges or diverges. If it
converges, find the limit. (If an answer does not exist, enter
DNE.)
an = (4^n+1) /
9^n

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