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docker41 [41]
3 years ago
12

Compute

i+i^2+i^3+\cdots+i^{258}+i^{259}" alt="i+i^2+i^3+\cdots+i^{258}+i^{259}" align="absmiddle" class="latex-formula">.
Mathematics
2 answers:
artcher [175]3 years ago
7 0

9514 1404 393

Answer:

  -1

Step-by-step explanation:

Alternate terms have a sum of zero:

  i^n +i^(n+2) = (i^n)(1 +i^2) = (i^n)(1 -1) = 0

So, the sum to i^256 is zero, and i^257 +i^259 = 0. The value of the sum is then i^258 = i^(258 mod 4) = i^2 = -1

The given expression evaluates to -1.

xz_007 [3.2K]3 years ago
3 0

Answer:

-1

Step-by-step explanation:

Note that i+i^2+i^3+i^4 = i-1-i+1 = 0, and this means that every 4 terms, the terms cancel to 0. Therefore, by taking modulo 4, we only need to find i^{257}+i^{258}+i^{259} = i-1-i = -1 since $i$ has a cycle of 4.

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Answer:

V₂ = 450 cm³

Step-by-step explanation:

The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P.

V\propto \dfrac{1}{P}

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We need to find a new volume. Using the above concept,

V_1P_1=V_2P_2\\\\V_2=\dfrac{V_1P_1}{P_2}\\\\V_2=\dfrac{600\times 300}{400}\\\\V_2=450\ cm^3

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An SRS of ten brands of breakfast cereals is tested for the number of calories per serving. The following data result: 185, 190,
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Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval estimate for the mean number of calories for servings of breakfast cereals is (195.3, 215.7).

<h3>What is a t-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm t\frac{s}{\sqrt{n}}

In which:

  • \overline{x} is the sample mean.
  • t is the critical value.
  • n is the sample size.
  • s is the standard deviation for the sample.

From the sample and the significance level of 0.05, we have that the parameters are given by:

\overline{x} = 205.5, s = 14.2, n = 10, t = 2.2622

Hence:

\overline{x} - t\frac{s}{\sqrt{n}} = 205.5 - 2.2622\frac{14.2}{\sqrt{10}} = 195.3

\overline{x} + t\frac{s}{\sqrt{n}} = 205.5 + 2.2622\frac{14.2}{\sqrt{10}} = 215.7

The 95% confidence interval estimate for the mean number of calories for servings of breakfast cereals is (195.3, 215.7).

More can be learned about the t-distribution at brainly.com/question/16162795

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Step-by-step explanation:

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