prove that f1 f3 f5 ... f2n-1=f2n

Answers

Answer 1

The proof shows that f1+ f3 +f5+ ... +f2n-1=f2n, Fibonacci number. This can be proven by using mathematical induction and manipulating the algebraic expression for the sum and the Fibonacci sequence.

We can prove this by mathematical induction.

Base case: When n = 1, the equation becomes f1 = f2 which is true.

Inductive step: Assume that the equation holds true for some value k, i.e., f1 + f3 + f5 + ... + f2k-1 = f2k.

We need to prove that the equation holds true for k+1, i.e., f1 + f3 + f5 + ... + f2(k+1)-1 = f2(k+1).

Adding f2k+1 to both sides of the equation for k, we get

f1 + f3 + f5 + ... + f2k-1 + f2k+1 = f2k + f2k+1

Now, we can use the identity that f2k+1 = f2k + f2k-1, which comes from the definition of the Fibonacci sequence. Substituting this, we get

f1 + f3 + f5 + ... + f2k-1 + f2k + f2k-1 = f2k + f2k+1

Rearranging and simplifying, we get

f1 + f3 + f5 + ... + f2k+1 = f2k+2

Therefore, the equation holds true for k+1 as well.

By the principle of mathematical induction, the equation holds true for all positive integer values of n. Hence, we have proved that f1 + f3 + f5 + ... + f2n-1 = f2n.

To know more about mathematical induction:

https://brainly.com/question/29503103

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--The given question is incomplete, the complete question is given

"Prove that f1+ f3 +f5+ ... +f2n-1=f2n"--


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What's the slope of the table

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Answer:

8 3 5 4 6 8 8 4 8 8. 8 8 8 8 8 8 8 7 7 7 7 77 7 4 4. 5 8

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What is the answer to -7X-8 =

Answers

Answer:

-7x-8=0

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x=-8/7

hope this helps

Answer:

The answer for -7 x -8 is 56

Step-by-step explanation:

two negatives equal one positive.

Simplify (4y - 3x - 2) - (7y + 4x + 3)

Answers

Answer:

-7x - 3y -5

Step-by-step explanation:

Answer:

-7x - 3y - 5

Step-by-step explanation:

In this question, you will simplify the expression given.

Solve:

(4y - 3x - 2) - (7y + 4x + 3)

Use the distributive property.

4y - 3x - 2 - 7y - 4x - 3

Combine like terms.

4y - 3x - 2 - 7y - 4x - 3

-7x + 4y - 2 - 7y - 3

-7x - 3y - 2 - 3

-7x - 3y - 5

Since we can't simplify further, your final answer would be -7x - 3y - 5

HELP PLEASE PLEASE PLEASE

Answers

Answer:

We'll need 2 points so we'll choose (-6, 0) and (0, -3).  

Let's calculate the slope (or 'm') using

Slope or m = (Y2 -Y1) ÷ (X2 -X1)

Slope ('m') = (-3 -0) / (0, - -6) = -3 / 6 = -1/2

Then we calculate the equation using:

(y - y1) = m • (x -x1)

(y - 0) = -1/2 * (x - -6)

y = -1/2 x -3

Source: http://www.1728.org/distance.htm

Step-by-step explanation:

Answer:

         x + 2y = - 6

Step-by-step explanation:

X-intercept:  (-6, 0)

Y-intercept:  (0, -3)    ⇒   b = -3

Slope:   [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{0+3}{-6+0}=-\dfrac12[/tex]

Slope-intercept form  y = mx + b

[tex]y=-\frac12x-3[/tex]        {multiply both sides by 2}

2y = - x - 6          {add x to both sides}

x + 2y = - 6

Please help. Due today.

Answers

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

because 2^ 3= 16 so you can pull it out.

Solve 3(x + 1) + 6 = 33

Answers

Answer:

3(X+1)+6=33

3x+3+6=33

3x+9=33

3x=33-9

X=24/3

X=8

Answer:

[tex]x = 8[/tex]

Step-by-step explanation:

1) Subtract 6 from both sides.

[tex]3(x + 1) = 33 - 6[/tex]

2) Simplify 33 - 6 to 27.

[tex]3(x + 1) = 27[/tex]

3) Divide both sides by 3.

[tex]x + 1 = \frac{27}{3} [/tex]

4) Simplify 27/3 to 9.

[tex]x + 1 = 9[/tex]

5) Subtract 1 from both sides.

[tex]x = 9 - 1[/tex]

6) Simplify 9 - 1 to 8.

[tex]x = 8[/tex]

Therefor the answer is, x = 8.

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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[tex]y=2x-7[/tex]

Step-by-step explanation:

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Step-by-step explanation:

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Steps:
Answer:

Answers

Answer:

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Step-by-step explanation:

The cereal box shown below is a rectangular prism. Find the surface area of the cereal box. ​

Answers

Answer:

580 cm^2

Step-by-step explanation:

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There are 2 sides with 20*10 ( front and back) so we can multiply by 2. 200*2=400

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420

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Answers

Answer:

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Answers

Answer:

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Step-by-step explanation:

Steve has 1 1/2 cups of flour. One of his recipes requires 1/8 cup of flour. What is the maximum number of times (batches) Steve can complete the recipe? a.2 3/4 b.16 1/2 c.20 or d.17

Answers

Answer:

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Step-by-step explanation:

Hello I am sorry to say but the answer should be 12 as 3/2÷1/8=12

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please mark me as brainlist

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Answer:

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Step-by-step explanation:

Answer:

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Saan po yung divisor?

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Answers

Answer:

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Step-by-step explanation:

For this type of albreic question you want to simplify

4x^2+14x+6=9x^2-6x+1

first you take the common integers(That might not be the right word)

4x^2+14x+6=9x^2-6x+1

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20x+5=5x^2

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O 1/8
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Answers

Answer:

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form

y*x=k or y= k/x

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pv=8

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v=8/p

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Priya is making burgers for a party. She has 5 pounds of meat and uses 1/3 of a pound for one burger. How many burgers can priya make?

Answers

Answer: Priya can make 15 burgers with 5 pounds of meat

Step-by-step explanation:

Step 1

From Priya's receipe,

1 burger can be made from  1/3 of a pound of meat  

  How many burgers can be made from 5 pound of meat

Step 2 Using the equation below, that

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Answers

Answer:

x > -3

Step-by-step explanation:

x + 8 > 5

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I hope this helped you :)


Solve for x:
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Answers

Answer:

X = 2

Step-by-step explanation:

First we'll need to simplify this equation:

Add 9x on both sides:

13x - 21 = 5

Add 21 on both sides:

13x = 26

Divide 26/13

26/13 = 2

X=2

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Using the following equation , solve the equation graphically for integral values of x any.
Plot a graph of the equations and shade out the area which is not in the range of values.

1.
[tex]y \geqslant 0 , \\ x - y \geqslant 1 , 3x + 4y < 12[/tex]

Answers

Answer:

See the attached

Step-by-step explanation:

y ≥ 0 - limits the region to first and second quadrantsx - y ≥ 1 ⇒ y ≤ x - 1 (region A on the graph)3x + 4y < 12 ⇒ y < - 4/3x + 4 (region B on the graph)

Regions covered by each functions are shaded and the intersection also shaded and marked.

The white area in the graph is the out of range region.

Answer:

  {(1, 0), (2, 0), (2, 1)}

Step-by-step explanation:

In the attached graph, the dashed lines are to be considered part of the unshaded area, hence in the solution set. The only points with integer coordinates in the solution set are the ones listed above.

A. 25-3x=40

Answer: x =
its a neg #

Answers

minus 25 on both sides which gives -3x = 15 divide by -3 which means x =-5

Answer:

-3x= 40-25

-3x=15

x=15÷3

x=5

Find the coordinates of the intersection of the diagonals of rectangle WXYZ with the given vertices. W (-1, 7), X (8,7), Y (6,-2), Z (-3,-2).

Answers

(-1,7) X (8,7) Y ( 6-2), ( -3 -2).

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