Question

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.

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?

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?

(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 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.

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.

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?

Use a power series to approximate the definite integral to 4
decimal places: from 0 to 1/2 (x^2)(e^(-x^2) dx. Find power series
of e^-x^2. and the value of the integral (how many terms
needed)

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...

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?

Summation from n=2 to infinity of ln(n)/n^2 * x^n
a.) Let x=-1, and compute the integral test to determine whether
this it is convergent or divergent
b.) Compute the ratio test to determine the interval of
convergence and explain what this interval represents.
I'm really confused with this problem (specifically a)- please
write out all of the details of computing the integral so I can
understand. Thank you!

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