Question

**Given the alternating series:***n=2**∞(**-1)^**n/***ln(***n)*

- (7 pts)
**Determine if the series converge**Use the fact that*absolutely*. (**:****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?**

Answer #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?

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

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.

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

1. Test the series below for convergence using the Root
Test.
∞∑n=1 (4n/10n+1)^n
The limit of the root test simplifies to lim n→∞ |f(n)| where
f(n)=
The limit is:
Based on this, the series
Diverges
Converges
2. We want to use the Alternating Series Test to determine if
the series:
∞∑k=4 (−1)^k+2 k^2/√k^5+3
converges or diverges.
We can conclude that:
The Alternating Series Test does not apply because the terms of
the series do not alternate.
The Alternating Series Test...

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...

Use the integral test to determine the divergence or convegence
of the series (1/ (ln(5))^n) ) I know it to be Convegence, unsure
how its convergent.

(a) Use any test to show that the following series is
convergent. X∞ n=1 (−1)n n 2 + 1 5 n + 1
(b) Find the minimum number of terms of the series that we need
so that the estimated sum has an |error| < 0.001.

Use any test to show that the following series is convergent. X∞
n=1 (−1)n (n2+ 1/ 5n + 1)
(b) Find the minimum number of terms of the series that we need
so that the estimated sum has an |error| < 0.001.

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