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PtichkaEL [24]
3 years ago
14

How do you do this question?

Mathematics
1 answer:
IRINA_888 [86]3 years ago
5 0

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.

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6. For a particular pickup truck, the percent markup is known to be 115% based on cost to the seller. If the seller paid $15,800
Neko [114]

Answer:

  • <u>53.5 %</u>

Explanation:

You can convert the percent markup into a multiplicative factor in this way:

Base price:                     15,800 . . . (cost to the seller)

Percent mark up:           115% . . .  (based on the cost to the seller)

Sale price:                      15,800 + 115% of x = 15,800 + 115 × 15,800 /100 =

                                        = 15,800 + 1.15 × 15,800 = 15,800 (2.15) = 33,970

The markup is:

  • Markup = price paid by the seller - cost to the seller = 33,970 - 15,800   = 18,170 (notice that this is 115% of 15,800)

And <em>the percent markup based on the sale price is</em>:

  • % = (markup / sale price) × 100 = (18,700 / 33,970) × 100 =

            = 53.49 %

Rounding to the nearest tenth percent that is 53.5 %.

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