# Search results

2. ### How do I show the following sequence is bounded above ?

Do you know about the harmonic numbers H_n~? and the the digamma function. Here are two webpages One & Two. The nth harmonic number is {H_n} = \sum\limits_{k = 1}^n {\frac{1}{k}} and your sequence turns out to be a_n=H_{2n}-H_n On the two references, you can find links to other research do by...
3. ### Still Confused

Of course I do not speak for Prof. Peterson, but \sqrt{25}=5 is one number. Now twenty has two square roots they are \pm\sqrt{25}=\pm5 For this prof in his complex variables classes this is what we use: "we add(enlargement of the reals) one number \mathit{i} that a solution for the equation...
4. ### The triangle midsegment theorem

Here completely different way to go. Say the vertices of the triangle are : A:\,(x_A,y_A),\,B:\,(x_B,y_B),~\&~C:\,(x_C,y_C) \begin{cases}\dfrac{x_A+x_B}{2}=-2 &,\quad \dfrac{y_A+y_B}{2}=0 \\\dfrac{x_A+x_C}{2}=0 &,\quad \dfrac{y_A+y_C}{2}=2 \\\dfrac{x_C+x_B}{2}=-4 &,\quad \dfrac{y_C+y_B}{2}=1...

6. ### How to demonstrate this inequality

|a-b|=|a+(-b)|=|(a-c)+(c-b)|
7. ### Geometric Sequences

Have you found the common ratio, r~? That is the terms of the sequence are g_n=60\cdot r^n,~n=0,~1,~2,\cdots. In your study have you learned limits like \mathop {\lim }\limits_{n \to \infty } \,{r^n} = ?
8. ### Area of a trapezoid in triangle.

Do you know the area of a trapezoid? Look here Now what Prof. Peterson calls "midline" is the upper base equal in length to half the other base. the midline also determines the height. Now post your work.
9. ### Is this right?

a^5b^{-\tfrac{1}{2}}(a+b)=a^6b^{-\tfrac{1}{2}}+a^5b^{\tfrac{1}{2}}
10. ### Lottery probability question

I am read this as if one can only one the four possibilities on any the five numbers on one ticket. So that is the sum of the four probabilities. that is winning exactly once.
11. ### Ayan and Naihan are twins. Ayan is the elder by 13 minutes. If Naihan was born on January 1, 2007 at 0005 hours, What is Ayan's date and time of birth

I hope that you read the posting guidelines. If you post your work it helps us help you. Now I assume that 0005 hours is five minutes after midnight on New Year's day. So work out 13 minutes before.
12. ### Lottery probability question

Because these events are mutually disjoint and independent the probabilities are additive. So apply that idea to both of these. You must post your work so we are allowed to help you understand.
13. ### What are the polar coordinates of (2√3, 2)?

This is the most important question: "What does your textbook/instructor say about polar coordinates?" As I said above I use the range -\pi<\theta\le\pi you may find this useful. For any point (x,y) where x\cdot y\ne 0 \arg(x , y) = \left\{ {\begin{array}{{ll}} {\arctan \left( {\frac{y}{x}}...
14. ### What are the polar coordinates of (2√3, 2)?

There is no hard and fast rule. But it is my preference that yours is the one that I would expect if I were your lecturer. The reason being that the form (r,\theta) where r>0~\&~-\pi<\theta\le \pi. You see r is the absolute value of the number and \theta its identifies location. Note some...

But that has absolutely nothing to do with the solution. This does: This image does The answer to the question is the area of the circle minus the area of the circular segment(green area) subtracted from the area of the circle.

I wonder if Prof Peterson could tell us about his solution? What did I miss?
17. ### Equality of quantities

Dear Ryan\$, you really need to enroll in a course that may go be many different names but it is philosophical logic. I think that I remember that you are in a area with several higher education units each of which has such a course. At the very least get yourself a copy of Copi's Symbolic Logic...
18. ### Semi-random team assignment

I would like to help with this. But I simply do not understand the setup. What does "will play in 7 rounds of 6 games" mean? If there are thirty-six players to be placed on teams of three players each then that is twelve teams and there are \dfrac{36!}{(3!)^{12}(12!)}=356765771022012352000000...
19. ### 2 proof questions help

1) Suppose that \begin{align*}\sqrt{m^2-n^2}&=m-n \\m^2-n^2&=m^2-2mn+n^2\\2mn&=0 \end{align*} What does that tell you about m\text{ and }n~? Is that a contradiction? 2) The roots of x^2-2bx+c=0 are x=\dfrac{2b\pm\sqrt{4b^2-4c}}{2}\text{ implies }x=b\pm\sqrt{b^2-c}. To have two real roots we...
20. ### Discrete Mathematics proof question help

I have wondered if promitheus were thinking of what Copi calls conditional proof? But that is for arguments in which the conclusion is itself a conditional statement. Speaking of Copi, in most of his texts he stresses these two statements. 1. A false statement implies any statement. 2. A true...