How do you do this question?

Mathematics

1 answer:

IRINA_888 [86]3 years ago

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Answer:

∑ (-1)ⁿ⁺³ 1 / (n^½)

∑ (-1)³ⁿ 1 / (8 + n)

Step-by-step explanation:

If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.

Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).

Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).

Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.

Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.

Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.

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Select all the correct answers.

Wittaler [7]

If the measure of angle θ is 3π/4, the true statements are:

sin(θ) = √2/2.
The measure of the reference angle is 45°.

<h3>How to determine the true statements?</h3>

In Trigonometry, an angle with a magnitude of 3π/4 (radians) is equivalent to 135° (degrees) and it's found in the second quarter. Thus, we would calculate the reference angle for θ in second quarter as follows:

Reference angle = 180 - θ

Reference angle = 180 - 135

Reference angle = 45°.

Also, a terminal point for this angle θ is given by (-√2/2, √2/2) which corresponds to cosine and sine respectively. This ultimately implies that sin(θ) = √2/2.

tan(θ) = cos(θ)/sin(θ)

tan(θ) = [(-√2/2)/(√2/2)]

tan(θ) = -1

In conclusion, we can logically deduce that only options A and B are true statements.

Read more on terminal point here: brainly.com/question/4256586

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Complete Question:

If the measure of angle θ is 3π/4, which statements are true. Select all the correct answers.

A. sin(θ)=sqrt2/2

B. The measure of the reference angle is 45

C. The measure of the reference angle is 30

D. The measure of the reference angle is 60