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3 years ago

Proof by mathematical induction

Mathematics

1 answer:

Ghella [55]3 years ago

5 0

Answer:

See below.

Step-by-step explanation:

I will assume that 3n is the last term.

First let n = k, then:

Sum ( k terms) = 7k^2 + 3k

Now, the sum of k+1 terms = 7k^2 + 3k + (k+1) th term

= 7k^2 + 3k + 14(k + 1) - 4

= 7k^2 + 17k + 10

Now 7(k + 1)^2 = 7k^2 +14 k + 7 so

7k^2 + 17k + 10

= 7(k + 1)^2 + 3k + 3

= 7(k + 1)^2 + 3(k + 1)

Which is the formula for the Sum of k terms with the k replaced by k + 1.

Therefore we can say if the sum formula is true for k terms then it is also true for (k + 1) terms.

But the formula is true for 1 term because 7(1)^2 + 3(1) = 10 .

So it must also be true for all subsequent( 2,3 etc) terms.

This completes the proof.

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Arada [10]

Answer:

Step-by-step explanation:

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-16 -16

4x = 8

/4 /4

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2 years ago

How many sides does a polygon have whose total number of diagonals is 20?

Bond [772]

Answer:

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3 years ago

Triangle A″B″C″ is formed using the translation (x + 2, y + 0) and the dilation by a scale factor of one half from the origin. W

Dafna1 [17]

Answer:

A. segment A double prime B double prime = segment AB over 2

Step-by-step explanation:

Triangle ABC with coordinates of:

A = (-3, 3), B = (1, -3), C = (-3, -3)

Translation (x + 2, y + 0), coordinates will be:

A' = (-1, 3), B = ( 3, -3), C = (-1, -3)

Dilation by a scale factor of 1/2 from the origin, coordinates will be:

A'' = (-0.5, 1.5), B'' = (1.5, -1.5), C= (-0.5, -1.5)

Let's find the length of AB and A''B'' using distance formula

d = √(x2-x1)² + (y2 - y1)²

AB = √(1-(-3))² + (-3 -3)² = √4²+6² = √16+36 = √52 = 2√13
A''B'' = √(1.5 - (-0.5)) + (-1.5 - 1.5)² = √2²+3² = √13

We see that

AB = 2A''B''

Now the answer options:

A. segment A double prime B double prime = segment AB over 2

Correct

B. segment AB = segment A double prime B double prime over 2

Incorrect. Should be AB = A''B''*2

C. segment AB over segment A double prime B double prime = one half

Incorrect. Should be AB/A''B'' = 2

D. segment A double prime B double prime over segment AB = 2

Incorrect. Should be A''B''/AB = 1/2

7 0

2 years ago

Read 2 more answers

the width of a rectangle is 3 units less than the length. if the area is 130 square units, then find the dimensions of the recta

Basile [38]

Answer:

Length = 10

Width = 13

Step-by-step explanation:

If the width of a rectangle is 3 units less than the length and if the area is 130 square units, the length is 10 units and the width is 13 units.

Formula: A=wl

Therefore, you have to find what two numbers multiply together in order to recieve 130 units.

A=wl=13·10=130

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3 years ago

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Makovka662 [10]

Depends on the type of AB, is it AB positive or AB negative

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6 0

3 years ago