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.
Solving for the missing variable
Sum is addition, less than is subtraction, equals is is, division is of and multiplication is per
The equation which represents the amount of money, y, that Lilia will save in x weeks is;
<h3>Slope-intercept form of linear equations</h3>
The slope-intercept form of linear equations usually takes the form;
According to the information given;
Therefore, the y-intercept of the equation is; $10.
- And since she saves $5 each week;
The slope of the equation is; $5.
By substitution, the required equation is;
Read more on slope-intercept form of equations;
brainly.com/question/1884491
