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.
Answer:
3
Step-by-step explanation:
15 divided by 5 equals 3.
Answer:
yes
Step-by-step explanation:
Answer:
There are 15 combinations.
Step-by-step explanation:
A restaurant is offering a dinner special that includes one starter and one entree.
Starter: bread-sticks, soup, salad
Entree: beef, fish, chicken, shrimp, pork
So, we have 3 starters and 5 entrees.
To know the possible dinner special combinations we will simply multiply the two.
Therefore, there are 15 combinations.
Answer: 216 ml
Step-by-step explanation:
400 grams = 480 ml
180 grams = ?
Since the value of 180 grams in milliliters is unknown, let the unknown be Z
Thus, 400 grams = 480 ml
180 grams = Z
To get the value of Z, cross multiply
Then, Z x 400 grams = 480ml x 180 grams
400Z = 86400
Divide both sides by 400
400Z/400 = 86400/400
Z = 216
Thus, 180 grams is equal to 216 milliliters.
