2 years ago

26.

Mathematics

1 answer:

Amiraneli [1.4K]2 years ago

5 0

Answer:

01201897397391789127897e8736296.2312

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Find S^20 if the series 1 + 1.1 ..... is a (a) arithmetic (b) geometric

quester [9]

I'm guessing S^20 is actually referring to the 20th partial sum $S_{20}$ , with

$S_{20}=1+(1+1\times0.1)+(1+2\times0.1)+\cdots+(1+18\times0.1)+(1+19\times0.1)$

in the arithmetic case, and

$S_{20}=1+1.1+1.1^2+\cdots+1.1^{18}+1.1^{19}$

in the geometric case.

(a) Combining like terms, we have

$S_{20}=20+0.1(1+2+\cdots+18+19)$

and invoking the formula

$1+2+\cdots+(n-1)+n=\dfrac{n(n+1)}2$

we end up with

$S_{20}=20+0.1\dfrac{19\times20}2=39$

(b) Multiply $S_{20}$ by 1.1, then subtract this from $S_{20}$ :

$1.1S_{20}=1.1+1.1^2+1.1^3+\cdots+1.1^{19}+1.1^{20}$

$S_{20}-1.1S_{20}=-0.1S_{20}=1-1.1^{20}$
$\implies S_{20}=\dfrac{1.1^{20}-1}{0.1}\approx57.275$

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3 years ago

What is the domain of the function graphed?

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D) all real numbers

Step-by-step explanation:

The domain is all real numbers because the graph continues to the left and right infinitely.

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Marnie purchased a dining room table and 6 chairs for $1,860.00 before discount and taxes. Kristen purchased a queen bed, dresse

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Add your two totals together,
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Step-by-step explanation:

2k - (3k - 3k) = 2k

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Gradient of a straight line that is perpendicular to y = 4x + 2

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If a line's slope is $\frac{a}{b}$ , the slope of the perpendicular line is $-\frac{b}{a}$
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