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"--


Related Questions

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I give brainliest to whoever answers correctly w/ an explanation first

answer the question below

i don’t get it, pls explain

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Where is the answer

помогите пж а то мне купец я не могу решить умоляю вас​

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Answer:

hshsjakaihshsksishshsjsiaiqoajsbsiwkajsvjsksjshshs

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

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

1 burger = 1/3 pound of meat

Therefore 5 pounds of meat

5 x 1 / 1/3 = 5/(1/3)

= 5 x3 = 15 Burgers.

-7X-8 =

What is the answer to -7X-8 =

Answers

Answer:

-7x-8=0

-7x=8

x=-8/7

hope this helps

Answer:

The answer for -7 x -8 is 56

Step-by-step explanation:

two negatives equal one positive.

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:

First, find the area of the front and back. 20*10=200

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

Then, the sides. 3*20=60*2=120

Then, the top and bottom 10*3=30*2=60

400+120+60=580

Answer:

420

Step-by-step explanation:

60+60+30+30+120+120

hope this helped :)

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


Solve for x:
(a) 4x - 21 = 5 - 9x​

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

(You can check this yourself by plugging x into the equation)

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:

12

Step-by-step explanation:

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

hope it helps you

please mark me as brainlist

What does the problem 37( 253,080 equal?​

Answers

Answer:

so confused like what is this

Step-by-step explanation:

Answer:

9363960

Step-by-step explanation:

The calculator says otherwise -.-

but yeah, hope it helps.

Solve and graph the inequality. Show all your work. Upload a picture of your work.

x + 8 > 5

Answers

Answer:

x > -3

Step-by-step explanation:

x + 8 > 5

   -8   -8

    x > -3

I hope this helped you :)

(4,1) slope = 2 , point slope form

Answers

Answer:

y-1=2(x-4)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=2(x-4)

Answer:

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

Step-by-step explanation:

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

Hope I helped!

Check out my profile for more answers!

Please help me solve this I have work and i can't have anything due late ..​

Answers

Answer:

the answer is C i hope this helps

Step-by-step explanation:

6(-5x - 16) = 30y + 84

Answers

Answer:
-6

Explanation:

James and Sarah went out to lunch. The price of lunch for both of them was $60. They tipped their server
25% of that amount
How much did each person pay if they shared the price of lunch and the tip equally?

Answers

Answer:

$37.50

Step-by-step explanation:

$60 x .25 = $15 (tip)

$60 (meal) + $15 (tip) = $75

$75 ÷ 2 (# of people splitting the cost) = $37.50

What is 4x^2+14x+6=9x^2-6x+1 answer

Answers

Answer:

20x+5=5x^2

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

       +6x  -1  -4x^2

20x+5=5x^2

You cannot simplify any further

Simplify x^6+10x^5+25x^4-x^2-10x-25 using synthetic division

Answers

Saan po yung divisor?

Kailangan ko po

TESTTT RNNNNnnnnnn WILL GIVE BRAINLESS

Answers

Answer:

iy7tfrdghjuygtfcvbnhjkiuytrfd

Step-by-step explanation:

The basketball team ordered two pizzas. They left 1/3 of one and 1/4 of the other uneaten. What amount of pizza did they have leftover?

Answers

Get both 1/3 and 1/4 to the same denominator, with is 12, you also multiply the numerator the same you had to as the denominator.

The answer is 7/12

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.

Kaylie bought 3 bags of milk for $14. Each bag had 4 litres of milk. What was the cost of milk per gallon?

Steps:
Answer:

Answers

Answer:

about 3 gallons

Step-by-step explanation:

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.

What's the slope of the table

Answers

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

I looks better also whats 7% of 798 explain

Answers

7% of 798 is 55.86.

Answer:

cappppppppppp

Step-by-step explanation:

jp wyd homie

Si al número de grados sexagesimales que contiene un ángulo se le resta 13, y a
un número de grados centesimales se le resta 2, se obtienen dos cantidades en la
relación de 2 a 3. ¿Cuál es la medida circular del ángulo?

Answers

Answer:

I am not sure my guy

Step-by-step explanation:

sorry?


For the inverse variation equation p=8/v what is the value of V when p = 4?
O 1/8
o 1/2
O 2
O 32

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

in this problem we have that

the value of the constant K is equal to 8

so

pv=8

Solve for V

v=8/p

Find the value of V for p=4

substitute the value of P in the formula

v=8/4=2

therefore

the answer is

the value of V is equal to 2

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).

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.

PLZ HELP!!! WILL GIVE HIGHEST POINTS IF THE ANSWER IS RIGHT!!

Answers

Step-by-step explanation:

Standard polynomial is:

[tex] - 20 {x}^{3} - 3 {x}^{2} + 4x[/tex]

Leading co effecient is:

-20

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