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Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

8 0

table A from 2-3 minutes it rose 64.9-61.3 = 3.6

from 3-7 it rose 79.3 -64.9 = 14.4 = 3.6 degrees per minute

Table B needs to raise faster than 3.6 per minute

64.4 -61 = 3.4

64.6 - 61 = 3.6

64.3 -60.6 = 3.7

so the 3rd table is correct

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IRINA_888 [86]

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.

5 0

3 years ago

I have a few questions:

inn [45]

Hello,
Please, see the attached files.
Thanks.