Question

Which of the following statements is true?

a) The geometric series Σ∞n=1 r^n is always convergent.

b) for the series Σ∞n=1an, if lim n→∞ an = 1/3, then the series will be convergent.

c) If an> bn for all values of n and Σ∞n=1 bn is convergent, then Σ∞ n=1an is also convergent.

d) None of the above

Answer #1

Suppose R>0. Which of the following statements might be true
about a power series centered about the point x=a
a) The series converges for all x>a
b) The series converges on the interval (a,R)
c)The series converges on the interval [a,R)
d) The series converges only at x=a+R
e) All of the above
f) None of the above

Suppose R>0. Which of the following statements might be true
about a power series centered about the point x=a
a) The series converges for all x>a
b) The series converges on the interval (a,R)
c)The series converges on the interval [a,R)
d) The series converges only at x=a+R
e) All of the above
f) None of the above

1.
Determine
whether the series is convergent or divergent.
a)
If
it is convergent, find its sum. (using only one of the THREE:
telescoping, geometric series, test for divergence)
summation from n=0 to infinity of
[2^(n-1)+(-1)^n]/[3^(n-1)]
b) Using ONLY
the
Integral Test.
summation from n=1 to infinity of
n/(e^(n/3))
Please give
detailed answer.

a) Is the following a geometric series??? Why? b) If it is,
determine if it is convergent or divergent. Why? c) If it is
convergent, find its sum; d) write the next three terms.
1/8 + 1/4 + 1/2 + 1...

1. Write a geometric series with a starting index of n = 0 which
has a sum of 4. Show how you come up with your series.
2. Using the geometric series you wrote in 1, show how you would
find the sum if the starting index was n = 3.
3. Write a geometric series that diverges.

1 - Which of the following statements is true regarding a 95%
confidence interval? Assume numerous large samples are taken from
the population.
a. In 95% of all samples, the sample proportion will fall within 2
standard deviations of the mean, which is the true proportion for
the population.
b. In 95% of all samples, the true proportion will fall within 2
standard deviations of the sample proportion.
c. If we add and subtract 2 standard deviations to/from the sample...

. A sequence { bn } is defined recursively bn= -bn-1/2, where b1
= 3. (a) Find an explicit formula for the general term of the bn =
f(n). (b) Is the sequence convergent or divergent? (c) Consider the
series ∑ approaches infinity and n=1 bn. Is this series
convergent or divergent? (d) If it is convergent, find its sum

(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.

1. Which of the following statements about the direction of a
magnetic force is always true? (Note: More than one answer choice
may be correct)
a)The direction of the magnetic force on a moving charged particle
is parallel to the direction of the external magnetic field.
b)The direction of the magnetic force on a moving charged particle
is parallel to the direction of the charged particle's
velocity.
c)The direction of the magnetic force on a moving charged particle
is perpendicular...

Which of the following are true statements?
The probability of an event is always at least 0 and at most
1.
The probability that an event will happen is always 1 minus the
probability that it won't happen.
If two events cannot occur simultaneously, the probability that
at least one event will occur is the sum of the respective
probabilities of the two events
a.
II only
b.
I only
c.
Only I and III are true statements
d.
I,...

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