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 can’t seem to look at the bottom two answers and the two ( A and B) are not correct. So you’re left with either C or D
U do the formula
slope = -9/4
Answer:
To obtain equivalent amount from both foods we can eat 10 ounces of Food I and 5 Ounces of food II
To obtain minimum cholesterol, the individual should eat only 21 ounces of food II and zero ounce of food for the daily supplement of the individual
Step-by-step explanation:
Food I contains 32×C + 10×E per ounce
Food II contains 20×C + 14×E
Here we have X × (Food I) + Y × (Food II) = 420 C + 170 E
32·X + 20·Y = 420 C
10·X + 14·Y = 170 E
Therefore
X = 10 and Y = 5
To minimize the cholesterol, we can increase amount of Food II to get
21 ounces of food II gives
420 units of vitamin E and 294 units of vitamin E with 273 units of cholesterol.
Answer:
y=6
Step-by-step explanation:
