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?

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

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.

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.

Consider the following series: lim n=1 to infinite 1 + 2n/ 3^n
(a) Determine the value of s2, the second partial sum. (b) Does the
series converge? Explain why or why not

Find a power series representation for the function.
f(x)=x^3/(x-8)^2
f(x)=SIGMA n=0 to infinity
Determine the radius of convergence
Use a Maclaurin series in this table to obtain the Maclaurin
series for the given function
f(x)=xcos(2x)

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...

a) Determine the series of the given function. In the first box
after the summation symbol, type in -1 or 1 indicating whether the
series is alternating or not.
b) Write out the sum of the first four nonzero terms of the series
representing this function.
c) Determine the interval of convergence. The outside boxes require
the endpoints and the inside boxes require the symbol < or
<=
1) ln(1-6x)
a) Series:
b) First 4 nonzeroes
c) within the interval...

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