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Llana [10]
3 years ago
13

Find the generating function for the sequence 1,-2,4,-8, 16, ...

Mathematics
2 answers:
kirill [66]3 years ago
3 0

Answer:

  a(x)=\dfrac{1}{1+2x}

Step-by-step explanation:

The generating function a(x) produces a power series ...

  a(x)=a_0+a_1x+a_2x^2+a_3x^3+\dots

where the coefficients are the elements of the given sequence.

We observe that the given sequence has the recurrence relation ...

  a_0=1;a_n=-2a_{n-1} \quad\text{for n $>$ 0}

This can be rearranged to ...

  a_n+2a_{n-1}=0

We can formulate this in terms of a(x) as follows, then solve for a(x).

\sum\limits^{\infty}_{n=1} {a_{n}x^n} =a(x)-a_0 \quad\text{and}\\\\\sum\limits^{\infty}_{n=1} {2a_{n-1}x^n} =(2x)a(x) \quad\text{so}\\\\\sum\limits^{\infty}_{n=1} {(a_n+2a_{n-1})x^n}=0=a(x)-a_0+2xa(x)\\\\a(x)=\dfrac{a_0}{1+2x}=\dfrac{1}{1+2x}

The generating function is ...

  a(x) = 1/(1+2x)

seropon [69]3 years ago
3 0

Answer:-3+double the number

Step-by-step explanation: It started off as -3 so to get the next answer you double the number and change the sign for each number.

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4.5 miles in 1 hour
7 0
3 years ago
Which phrase best describes this polygon?
EleoNora [17]

Answer:

Concave octagon

Step-by-step explanation:

Concave octagon:

  • This polygon has 8 sides. So it is a octagon.
  •  If one interior angle measures more than 180, then it is concave polygon.  

So, this is a concave octagon

8 0
2 years ago
Find the surface area of composite figure. Please help
Ivan

Answer:

The surface area of the composite figure is 410\ m^{2}

Step-by-step explanation:

we know that

The surface area of the composite figure is equal to the surface area of the rectangular prism of the bottom plus the lateral area o the rectangular prism of the top

so

Step 1

Find the surface area of the rectangular prism of the bottom

The surface area is equal to

SA=2B+Ph

Find the area of the base B

B=10*10=100\ m^{2}

P=4*10=40\ m

h=3\ m

substitute

SA=2(100)+40(3)=320\ m^{2}

Step 2

Find the lateral area of the rectangular prism of the top

The lateral area is equal to

LA=Ph

P=2*(4+5)=18\ m

h=5\ m

substitute

LA=18(5)=90\ m^{2}

Step 3

Find the surface area of the composite figure

320\ m^{2}+90\ m^{2}=410\ m^{2}

8 0
3 years ago
Round 120 to the nearest whole percent
Ahat [919]
Its 100 because its not rounded to the nearest whole like 200 because its less than 50 so it would round down
3 0
3 years ago
2. Write the equation of the line perpendicular to 3x-4y=7 and passing through (0,0).​
Alenkinab [10]

Answer: y=-4/3x

Step-by-step explanation: opposite reciprocal

4 0
3 years ago
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