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alukav5142 [94]
2 years ago
7

Which of the below options shows the correct format for scientific

Mathematics
1 answer:
aev [14]2 years ago
7 0

(b) 1

(c) 34.765 x 10^-4

(d)  2.56 x 10^2

<u>Explanation:</u>

Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form.

In this case, the scientific notation of 00.0602 will be 6 X 10⁻⁴

1 , 34.765 x 10⁻⁴  and 2.56 x 10² are already in scientific notation form.

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A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021
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The sum of the given series can be found by simplification of the number

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  • A is approximately <u>2020.022</u>

Reasons:

The given sequence is presented as follows;

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Therefore;

  • \displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}

The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;

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  • \displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}

2 × 2043231 = n² + 3·n + 2

Which gives;

n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0

Which gives, the number of terms, n = 2020

\displaystyle \frac{A}{2}  = \mathbf{ 1011 \cdot  \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460}  \right)}

\displaystyle \frac{A}{2}  = 1011 \cdot  \left(1 - \frac{1}{2} +\frac{1}{2} -  \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022}  \right)

Which gives;

\displaystyle \frac{A}{2}  = 1011 \cdot  \left(1 - \frac{1}{2022}  \right)

\displaystyle  A = 2 \times 1011 \cdot  \left(1 - \frac{1}{2022}  \right) = \frac{1032231}{511} \approx \mathbf{2020.022}

  • A ≈ <u>2020.022</u>

Learn more about the sum of a series here:

brainly.com/question/190295

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