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2 years ago

5. Evaluate the series 50 + 10 + 2 + . . . 62 The series diverges; it does not have a sum. 62.5

Mathematics

1 answer:

Serga [27]2 years ago

7 0

Answer:

62.5

Step-by-step explanation:

By dividing 50 by 10 and 10 by 2 we can find that <em>r</em>, or the common ratio is 1/5, meaning that this series converges, so it is solvable. The formula for a convergent series is $\frac{a_{1}}{1-r}$ . By plugging in 1/5 for <em>r</em> and 50 for $a_{1}$ we can find that the sum of this infinite series is 62.5

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$5;\ 5;\ 5;\ 5;\ 7;\ 9\\\\\overline{x}=\dfrac{5+5+5+5+7+9}{6}=\dfrac{36}{6}=6\\\\\delta^2=\dfrac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+(x_3-\overline{x})^2+...+(x_n-\overline{x})^2}{n}\\\\\delta^2=\dfrac{(5-6)^2+(5-6)^2+(5-6)^2+(5-6)^2+}{6}$
$\dfrac{+(7-6)^2+(9-6)^2}{6}\\\\\delta^2=\dfrac{(-1)^2+(-1)^2+(-1)^2+(-1)^2+1^2+3^2}{6}=\dfrac{14}{6}=\dfrac{7}{3}$

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