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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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Hope this Helps! :)

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