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Nonamiya [84]
3 years ago
11

What is wrong with this "proof"? "Theorem" For every positive integer n,n i =1 i = (n + 1 2 ) 2 /2. Basis Step: The formula is t

rue for n = 1. Inductive Step: Suppose thatn i=1 i = (n + 1 2 ) 2 /2. Then n+1 i=1 i = ( n i=1 i) + (n + 1). By the induc-tive hypothesis, n+1 i=1 i = (n + 1 2 ) 2 /2 + n + 1 = (n 2 + n + 1 4 )/2 + n + 1 = (n 2 + 3n + 9 4 )/2 = (n + 3 2 ) 2 /2 =[ (n + 1) + 1 2 ] 2 /2, completing the induc-tive step.
Mathematics
1 answer:
creativ13 [48]3 years ago
7 0

Answer:

The basis step is not even true.

Step-by-step explanation:

The basis step would be for     n = 1.

If the basis step was true then you would have that.

\sum\limits_{i=1}^{1} i  =  \frac{(1+1/2)^2}{2}

Now. When you say

                                            \sum\limits_{i=1}^{1}  i            

That's just a fancy way of writing    1.  

On the other hand    

\frac{(1+1/2)^2}{2}  = \frac{9}{4} = 2.25

Therefore  

  1 \neq 2.25

And the basis hypothesis is false.

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kotykmax [81]

Answer:

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Step-by-step explanation:

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3 0
3 years ago
Instructions: Complete each question by choosing or typing in the best answer.
kupik [55]

The sum of 38 and twice a number x is 124. The value of "x" is 43

- 2x - 5 is equal to – 91.

<u>Solution:</u>

Given that , The sum of 38 and twice a number x is 124.  

We have to find what is - 2x - 5?

Now, according to given information, 38 + 2 × x = 124  

2x + 38 = 124  

2x = 124 – 38  

2x = 86  

x = 43

So, the value of x is 43

<em><u>Now, Evaluating - 2x – 5  </u></em>

Substitute "x" = 43 to evaluate

- 2(43) – 5  

- 86 – 5  = - 91

Hence, the required answer is – 91.

5 0
4 years ago
What is the area of a quadrilateral with vertices of (2,-4) (4,-4) (2,1) and (4,1)
taurus [48]

if you draw it out, it is a vertical rectangle

height of rectangle= 1-(-4)= 5units

length of rectangle= 4-2= 2units

area of rectangle =2×5= 10units^2

4 0
3 years ago
As a pharmacist, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your re
solmaris [256]

110/154 = x/126

154x/13860

x = 13860 /154 = 90

 90 milligrams of medicine A

6 0
3 years ago
Read 2 more answers
Area and circumference of a circle with a diameter of 2 yd
AlladinOne [14]

Hi there,

Here is the formula that you need to use to solve for the circumference and the area of a circle.

C = \pi d= 2\pi r     \\A = \pi r^{2}

So in this case, r is the radius of the circle

Thus,

d = 2 == > r = \frac{2}{2} = 1\\C = 2\pi * 1 = 2\pi

Now we do the math, to get to:

C = 6.28 (approximately, and you only need to keep it to 2 decimal places)

So 6.28 is the circumference, but now we need to find the Area

A = \pi * 1^2 = \pi  

So Area = 3.14 (approximately, to 2 decimal places)

Thus the answers are:

The circumference is 6.28 yards and the Area is 3.14 Square years

Please 5 stars and a like if you find this answer helpful.

Happy to help!

6 0
2 years ago
Read 2 more answers
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