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:
Step-by-step explanation:
Equation : 165 = 102 + 1.4K
Define: K is # of kilometers
Solve: 63 = 1.4k, so k = 45
Final answer: 45 kilometers
B=(32)(1700) your answer should be 54,400 BTU's
Answer:
The perimeter is 30 units
Step-by-step explanation:
To find the perimeter of SOW, what we need to do is to add all the lengths around the triangle together.
But we only have OS, we do not have OW and WS. Thus , we need to get what the values of these lengths are before we can calculate the perimeter.
Please check the attachment for complete solution.
