3 years ago

Please do this no fake stuff please. Click on the paper clip to see the problems stay safe

Mathematics

2 answers:

IRISSAK [1]3 years ago

7 0

25/372
26/936
27/56,21
28/30,54

pychu [463]3 years ago

5 0

25) 372
26)936
27) 58.1
28)35.4
29)10x+17
30)9a
31)-16m+11
32)44n-24

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Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

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3 years ago

Determine which of these illustrates two quantities that combine to make 0.

Butoxors [25]

I think it’s gonna be D

6 0

3 years ago

PLEASE HELPPppp

sasho [114]

Answer: B

Hope this helps :)

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2 years ago

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patriot [66]

(0,-5) and (3,-4) Hope this helps

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3 years ago

Rewrite the polynomial 2x2 + x + +-7x + 1 in standard form.

sveticcg [70]

Answer:

x-7x+5

Step-by-step explanation:

4+x-7x+1

x-7x+5

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2 years ago