| INFINITE SURDS | Ria Garg | | The purpose of my investigation is to find the general statement that represents all values of k in an infinite surd for which the expression is an integer. I was able to achieve this goal through the process of going through various infinite surds and trying to find a relationship between each sequence. In the beginning stages of my investigation I came across the sequence of ` a1= 1+1 a2= 1+1+1 a3 = 1+1+1+1 While looking at the sequence I came to the realization that there is a very obvious pattern between each n value. The answer to each n value was plugged into the next n value. For example if you look at this sequence a1= 1+1 = 1.414213562 a2= 1+1+1 = …show more content…
Also since the sequence is a square root and, the graph shows no evidence of a root value I can disregard the negative answer to the infinite surd. x=-b±b2-4ac2a X=1+1-41-121 x=1+52 Now, I would like to carry on my investigation and look at another sequence of infinite surds where the first term of the sequence is 2+2. In the beginning steps of my investigation I came up with the formula an+1 = 1+an, which I will be using to further my investigation and find the first 10 terms of my new sequence. A1 = 2+2 a6 = 2+a5 = 1.847759065 = 1.999962351 a2 = 2+a1 a7 = 2+a6 = 1.961570561 = 1.999990588 a3 = 2+a2 a8 = 2+a7 = 1.990369453 = 1.999997647 a4 = 2+a3 a9 = 2+a8 = 1.997590912 = 1.999999412 a5 = 2+a4 a10 = 2+a9 = 1.999849404 = 1.999999853 Repeating the same process I completed with the previous sequence of infinite surds, for the next step I will consider the value of an – an+1
Create 2 formulas, one that will calculate the last number in terms of the first number and a constant increase in rate as well as the total amount of numbers. The second formula will add ass of the resulting numbers from the first formula together after the last number is calculated.
The square root of 16 is 4 and 4 is an integer, rational number, whole number, natural numbers.
| 11. Is the sequence 5, 9, 15, ... an arithmetic sequence? Explain. Type your answer below.
Overflow occurs when the two numbers of similar signs are added together and a result with an opposite sign is produced.
1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 18, 21, 19, 26
Imagine the number eight. People would probably think that it’s just eight and nothing but eight. Now imagine the number eight tilted 90° to the left. People now see the infinity symbol. Now, people would probably think of it as an expanding number that never ends.
In this assignment I would like to talk about arithmetic sequences and geometric sequences and want to give an example each how to calculate with those sequences. First I want to give a short definition of each sequence.
Three of your friends, Anna, Blake, and Christine, run to you to settle a dispute. They were simplifying a radical expression into an exponential expression, but they reached different answers. Wisely, you decide to look at their work to see if you can spot the source of confusion.
public double goldenRatioSeq(int n) { if (n == 1) return 1; else return 1 + 1 / goldenRatioSeq(n - 1); }
Over the course of human events, men and women of all ages fought and worked relentlessly to better their lives and their families' lives as well. Despite the arduous efforts, each and every one of those people ended up or will end up exactly the same: buried six feet under the ground. Life and death are the largest eventualities to happen to humans as a whole, yet most sentient beings, particularly humans, are afraid of death, due mainly to the natural fear of the unknown. "Numbers" by Mary Cornish seems to beg the question of what does it mean to truly be alive. Being alive is to expand horizons and to feel what life has to offer or simply to be happy, but in layman's terms, life is more than just being born, surviving and finally dying.
) Determine whether each of these set is finite, countably infinite, or uncountable. Justify your answer
Radical formulas are used in many fields of the real world; some examples are in finance, medicine, engineering, and physics. These are just a few. In the finance department they use it to find the interest, depreciation and compound interests. In medicine it can be used to calculate the Body Surface of an adult (BSA), in engineering it can be used to measure voltage. These formulas are vital and important to the people working in these fields of work. Our week 3 assignment requires that we find the capsizing screening value for the Tartan 4100, solve the formula for variable of d, and find
3 4 167 0.075 1,060 0.48 204 241 — 340 213 1.0 0.3 59.2 10.7 0.20 63.5 1,124 521 22.5 3,293 98,100 624 16 22 5 19 — 974 944 11,511 48
2 25 18 36 35 40 48 51 77 80 99 71 69 43 42 46 54 67 45 45 29 12
The implications of infinity (co) are actualiy not that old. The Greeks were some of the first mathematicians recorded to have imagined the concept of infinity. However, they did not actuaily delve into the entirety of this number. The Greeks used the term “potentially infinite," for the concept of an actual limitless value was beyond their comprehension. The actual term “infinity” was defined by Georg Cantor, a renowned German mathematician, in the late nineteenth century. It was originally used in his Set Theory, which is a very important theory to the mathematical world. The value of infinity can get a bit confusing, as there are different types of infinity. Many claim that infinity is not a number. This is true, but it does have a value. So, infinity may be used in mathematical equations as the greatest possible value. i The value of infinity Infinity (00) is the greatest possibleivalue that can exist. However, there are different infinities that, by logic, are greater than other forms of itself. Here is one example: to the set of ait Naturai numbers Z43, 2, 3, 4,...}, there are an infinite amount of members. This is usualiy noted by Ko, which is the cardinality of the set of alt natural numbers,