Question

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?

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?

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?

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 (-1)^n/n! do you need to add up for
the partial sum to be at most 0.00001 away from the true sum of the
series? What is the value of the partial sum?

Approximate the sum of the series correct to four decimal
places, ((-1)^n-1*n^2)/12^n

Let Sum from n=1 to infinity (an) be a convergent
series with monotonically decreasing positive terms. Prove that
limn→∞ n(an) = 0.

Mark each series as convergent or divergent
1. ∑n=1∞ln(n)4n
2. ∑n=1∞ 4+8^n/2+3^n
3. ∑n=1∞ 6n/(n+3)
4. ∑n=1∞1/(7+n2−−√6)
5. ∑n=3∞ 6/(n^4−16)

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

Compute ln(2) with an error less than 10^-7. Find the number of
terms needed to be used from the series.

find the sum of the series
sigma n=0 to infinity {2 [3^(n/2 -2) / 7^(n+1)] + sin ( (n+1)pi
/ 2n+1) - sin (n pi / 2n-1)}

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