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: $216
Step-by-step explanation:
Hope it helped
The answer would be two grams of honey, because 1 gram of honey would make 1 half pan (because 6 is half of 12) So therefore, two grams of honey would make one pan of pudding.
Answer:
Step-by-step explanation:
Koris current age = x
Josephs current age = 7 + x
Koris age after four years = x + 4
Josephs age after four years = 7 + 4 + x = 11 + x
In 4 years the sum of their ages will be 75.
So, (x + 4) + (11 + x) = 75
= 2x + 15 = 75
2x = 75 - 15
x = 60/2 = 30
Therefore koris current age = 30
Josephs current age = 30 + 7 = 37
Hope this helps . Have a nice day!
Answer:
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Step-by-step explanation:
