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.
I believe it's 5 to 9 since out of 9 games they win 5 and lose 4. This doesn't account for draws or anything, though.
Answer: 133 windows
Step-by-step explanation:
Step 1: 38/2=19
Step 2: 19*7=133
Stan's, Mark's and Wayne's ages are 35 , 36 and 37 years respectively.
<em><u>Explanation</u></em>
Stan's, Mark's and Wayne's ages are <u>consecutive whole numbers</u> and Stan is the youngest and Wayne is the oldest.
So, lets assume that Stan's, Mark's and Wayne's ages are 
and 
Given that, the sum of their ages is 108. So, the equation will be.....
So, Stan's age is 35 years , Mark's age is (35+1)= 36 years and Wayne's age is (35+2)= 37 years.
For the answer to the question above asking to f<span>ind the coordinates of Z without using any new variables.
</span>
Vector WZ equals vector VP, which is (p, -q)
So Z is (-p - r + p, q - q) which is (-r, 0)
I hope my answer helped you.
