Question

**Given the alternating series:****sigma***(2 to infinity): (-1)^n / ln n*

**Determine if the series converge**Use the fact that*absolutely*. (**:****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?**

Answer #1

Given the alternating
series:
n=2∞(-1)^n/ln(n)
(7 pts) Determine if the series converge
absolutely. (Use the fact
that: ln n <
n )
(7 pts) Determine if the series converge
conditionally.
(7 pts) Estimate the sum of the infinite series using
the first 4 terms in the series and estimate the
error.
(7 pts) 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?

determine whether the alternating series ∑ (1 to ^ infinity)
(-1)^(n+1) 3^n / (n +1)! is absolutely convergent, conditionally
convergent or divergent.

How many terms of the series n=2 to infinity 12/(6n ln(n)^2)
would you need to approximate the sum with an error less than
0.02?

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

how do I show if the series sigma(n=1 to infinity)
cos(npi/3)/(n!) is divergent, conditionally convergent, or
absolutely convergent?

Infinity Sigma n=1 (n+1 / n^7/3 + sqrt n)
Does this series converge or diverge?

Consider the series: ∞∑n=21n[ln (n)]4 a) Use the integral test
to show that the above series is convergent b) How many terms do we
need to add to approximate the sum with in Error<0.0004.

Determine whether the given series are absolutely convergent,
conditionally convergent or divergent: a.) sigma ∞to n=0 (−3)n\(2n
+ 1)!
b.) sigma ∞ ton=1 (2n)!\(n!)2

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.

Given: Sigma (infinity) (n=1) sin((2n-1)pi/2)ne^-n
Question: Determine if the series converges or diverges
Additional: If converges, is it conditional or absolute?

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