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kirza4 [7]
3 years ago
6

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

ot show that Rn(x) → 0.] Find the associated radius of convergence R. f(x) = 6(1 − x)−2
Mathematics
1 answer:
weeeeeb [17]3 years ago
6 0

I guess the function is

f(x)=\dfrac6{(1-x)^2}

Rather than computing derivatives of f, recall that for |x|, we have

g(x)=\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n

Notice that

g'(x)=\dfrac1{(1-x)^2}

so that f(x)=6g'(x). Then

f(x)=6\displaystyle\sum_{n=0}^\infty nx^{n-1}=6\sum_{n=1}^\infty nx^{n-1}=6\sum_{n=0}^\infty(n+1)x^n

also valid only for |x|, so that the radius of convergence is 1.

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Izracunaj opseg i povrsinu kruga upisanog u kvadrat stranice duljine 8 cm.
Nutka1998 [239]
(In English), your question would state the following:


<span>Calculate the circumference and circumference of the circle entered in a square 8 cm long.
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So when finding the answer this this question, we know that the circumference would be the complete area of a circle.

So, I believe we would want to find what is the radius and the diameter that would make this circumference 8^c^m.

The radius would then be (1.274).
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Now in your own language (Croatian).

<span>Dakle, kad pronađemo odgovor na ovo pitanje, znamo da bi opseg bio cjelokupno područje kruga. Dakle, vjerujem da bismo željeli otkriti što je radijus i promjer koji bi ovaj opseg mogao učiniti 8cm. Radijus bi onda bio (1.274).</span>




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3 years ago
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The numbers 1 to 12 must be placed in the circles of the star shown on the right. The sums of the numbers in each row, and the s
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Answer:

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So the 34.55 were deduced from this number, and the remaining amount was:

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