1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = 1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> + <em>i </em>² + <em>i</em> ³)
… = 1 + <em>i </em>+ <em>i</em> ² (1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> + (-1) (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> - 1 - <em>i</em> )
… = 1 + <em>i</em>
<em />
Alternatively, notice that
1 - <em>i</em> ⁶ = (1 - <em>i</em> ) (1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵)
so that
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - <em>i</em> ⁶) / (1 - <em>i</em> )
Now, <em>i</em> ⁶ = (<em>i</em> ²)³ = (-1)³ = -1, so
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - (-1)) / (1 - <em>i</em> )
… = 2 / (1 - <em>i</em> )
Multiply the numerator and denominator by the conjugate of 1 - <em>i</em> :
… = 2 (1 + <em>i</em> ) / ((1 - <em>i</em> ) (1 + <em>i</em> ))
… = 2 (1 + <em>i</em> ) / (1² - <em>i</em> ²)
… = 2 (1 + <em>i</em> ) / (1 + 1)
… = 1 + <em>i</em>
Answer:
true
Explanation:
Uruguay has, according to UNESCO, a literacy rate of 98.62% that grows year by year. The female literacy rate is higher than the male.
The conclusion that the writer should add to summarize the argument of the passage is: "Hence, more schools should follow the trend of starting later in the morning if they want to see improved test scores, greater attendance numbers, and, most importantly, healthier, happier teens."
<h3>Meaning of a text's conclusion</h3>
The conclusion of a text is the final part of the text where the author summarizes the main ideas of the text.
The text above encourages the opening of schools later to help students enjoy longer hours of sleep. The conclusion beginning with the transition, "hence" aptly summarizes this point.
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The incidences are:
Kevin Prince Boaten, a football player from Ghana, was constantly noticed because of his black race.
<h3>How does racism influence participation in sport?</h3>
Others are:
- Jackie Robinson, experienced being criticized for his black color but he was said to be the first African-American player.
- Anthony Mundaine was a player in Australia who opt for boxing instead of being in the Rugby League as a result of racial discrimination.
Racism is known to be a major to participation in sports. Note that as a result of people experiencing discrimination, there may be a reduction in the people's participation in it.
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