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:
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--The given question is incomplete, the complete question is given
"Prove that f1+ f3 +f5+ ... +f2n-1=f2n"--
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:
Answer:
about 3 gallons
Step-by-step explanation:
Simplify x^6+10x^5+25x^4-x^2-10x-25 using synthetic division
Saan po yung divisor?
Kailangan ko po
What does the problem 37( 253,080 equal?
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.
What is 4x^2+14x+6=9x^2-6x+1 answer
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
6(-5x - 16) = 30y + 84
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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
Solve for x:
(a) 4x - 21 = 5 - 9x
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)
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]
Answer:
See the attachedStep-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.
помогите пж а то мне купец я не могу решить умоляю вас
Answer:
hshsjakaihshsksishshsjsiaiqoajsbsiwkajsvjsksjshshs
A. 25-3x=40
Answer: x =
its a neg #
Answer:
-3x= 40-25
-3x=15
x=15÷3
x=5
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?
Answer:
I am not sure my guy
Step-by-step explanation:
sorry?
Solve and graph the inequality. Show all your work. Upload a picture of your work.
x + 8 > 5
Answer:
x > -3
Step-by-step explanation:
x + 8 > 5
-8 -8
x > -3
I hope this helped you :)
What's the slope of the table
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
Please help me solve this I have work and i can't have anything due late ..
Answer:
the answer is C i hope this helps
Step-by-step explanation:
Please help. Due today.
Answer:
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
because 2^ 3= 16 so you can pull it out.
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?
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
The cereal box shown below is a rectangular prism. Find the surface area of the cereal box.
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 :)
TESTTT RNNNNnnnnnn WILL GIVE BRAINLESS
Answer:
iy7tfrdghjuygtfcvbnhjkiuytrfd
Step-by-step explanation:
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?
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.
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
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
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?
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
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
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
HELP PLEASE PLEASE PLEASE
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 = - 6Step-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
(4,1) slope = 2 , point slope form
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!
Solve 3(x + 1) + 6 = 33
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.
Simplify (4y - 3x - 2) - (7y + 4x + 3)
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
I looks better also whats 7% of 798 explain
Answer:
cappppppppppp
Step-by-step explanation:
jp wyd homie
PLZ HELP!!! WILL GIVE HIGHEST POINTS IF THE ANSWER IS RIGHT!!
Step-by-step explanation:
Standard polynomial is:
[tex] - 20 {x}^{3} - 3 {x}^{2} + 4x[/tex]
Leading co effecient is:
-20
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).
(-1,7) X (8,7) Y ( 6-2), ( -3 -2).
-7X-8 =
What is the answer to -7X-8 =
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.