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This is instead a sum of a smaller amount the people could have paid ($9 × 3 people = $27), added with the additional money that the clerk would not have needed had they paid that smaller amount ($27 paid - $25 actual cost = $2). Another way to say this is, the $27 already includes the bellhop's tip.
The idea becomes clearer by considering the general series 1 − 2 x + 3 x2 − 4 x3 + 5 x4 − 6 x5 + &c. that arises while expanding the expression 1⁄(1+x)2, which this series is indeed equal to after we set x = 1.
In order to transform the series 1 + 2 + 3 + 4 + ⋯ into 1 − 2 + 3 − 4 + ⋯, one can subtract 4 from the second term, 8 from the fourth term, 12 from the sixth term, and so on.
The ninth generation of video game consoles began in November 2020 with the releases of Microsoft's Xbox Series X and Series S console family and Sony's PlayStation 5. ...
1 − 2 + 4 − 8 + ⋯ In mathematics, 1 − 2 + 4 − 8 + ⋯ is the infinite series whose terms are the successive powers of two with alternating signs. As a geometric series, it is characterized by its first term, 1, and its common ratio, −2.
10, 9, 8, 7, 6, 5, 4, 3, 2, 1 is the fourth studio album by Midnight Oil that was released on vinyl in 1982 under the Columbia Records label. It peaked at No. 3 on the Australian Kent Music Report Albums Chart and remained on the chart for 171 weeks. [1] It also became the band's first album to be released in the US, where it peaked at number 178 on the Billboard 200 .
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1747 Olentangy River Rd, Columbus, OH · Directions · (614) 299-9425