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ra1l [238]
3 years ago
5

−1/5a+9/5a+6 =30 solve for a

Mathematics
1 answer:
Nonamiya [84]3 years ago
7 0

Answer:

a=15

Step-by-step explanation:

Solve for  a  by simplifying both sides of the equation, then isolating the variable.

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Find the generating function for the sequence 1,1,1,2,3,4,5,6,....
marin [14]

Answer:

P(x)=\dfrac{1}{1-x}+\dfrac{x^3}{(1-x)^2} \quad \text{for} \mid x \mid < 1[/tex]

Step-by-step explanation:

The generating function of a sequence is the power series whose coefficients are the elements of the sequence. For the sequence

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the generating function would be

P(x)=1+x+x^2+2x^3+3x^4+4x^5+5x^6+...\\

we can multiply P(x) by x to get

xP(x)=x+x^2+x^3+2x^4+3x^5+4x^6+...

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P(x)-xP(x)=1+(2x^3-x^3)+(3x^4-2x^4)+(4x^5-3x^5)+(5x^6-4x^6)+...\\   \\=1+x^3+x^4+x^5+x^6+...=1+x^3(1+x+x^2+x^3+x^4+...)

which for \mid x \mid < 1 can be rewritten as

(1-x)P(x)=1+\dfrac{x^3}{(1-x)} \quad \Rightarrow \\\\P(x)=\dfrac{1}{(1-x)}+\dfrac{x^3}{(1-x)^2}

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