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Anni [7]
3 years ago
6

Show that the series is convergent by the alternating series test, and find the number of terms necessary to estimate the sum of

the series with an error of less than 0.05.

Mathematics
1 answer:
Murljashka [212]3 years ago
7 0

Answer:

6 terms

Step-by-step explanation:

2 − 2/4 + 2/9 − 2/16 + ...

∑ (-1)ⁿ⁺¹ 2 / n²

Applying alternating series test:

lim(n→∞) 2/n² = 0

2/(n+1)² < 2/n², so the series is decreasing.

Therefore, the series converges.

2/(n+1)² < 0.05

(n+1)²/2 > 20

(n+1)² > 40

n+1 > 6.32

n > 5.32

n = 6

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You invest a total of $5800 in two investments earning 3.5% and 5.5% simple interest. Your goal is to have a total annual intere
attashe74 [19]
The annual interest that can be earned through investment of an amount at a simple interest can be calculated through the equation,
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Heyguys can soeom plzz help meee?? IDK how to do this!! 20 Points? plz write all details of the problem plzz!
marin [14]

Answer:

The distance travelled is 7.98×10³ miles.

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d = 7.98 \times  {10}^{3} miles

3 0
3 years ago
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