Recent content by DEMJR

I want to find x for (1) and x and y for (2). I am not sure how to put the images directly into the thread so I apologize if you do not like having to click on them. On the first one, I do not know how we can find this without knowing that XW is a diameter (it is not given as one in the...

Thanks. I see the pattern and realize my mistake in my previous post (so silly of me). I did it for the next few terms and got it to be 1 - 2x + 3x^2 - 4x^3 + 5x^4 - 6x^5 How can I use the pattern to integrate termwise between 0 and x? I forgot to mention in the original post that we are...

Not sure if I correctly implemented your response but here is what I tried: 1/(1+x) = 1 + 1/x -x/(1+x) = -x - 1 x^2/(1+x) = x^2 + x -x^3/(1+x) = -x^3 - x^2 However, this seems to be incorrect because everything cancels except the 1/x 1/(x+1) = 1 + 1/x - x - 1 + x^2 + x -x^3 -...

Not sure when this problem in my book says to calculate by long division the series 1/(1+x) = 1 - x + x^2 - x^3 + ..., and then integrating termwise between 0 and x. I am really rusty on these types of problems and need help understanding how to even begin T.T. Thanks for the help.

I want to prove x^3 + a^2x + b^2 = 0 has one negative and two imaginary roots if b \not= 0. I know that it cannot have any positive real roots because a > 0 and b > 0 will always be the case. I believe I can prove this using Descarte's Rule of Signs (which is in the same chapter of this...

This is a proposition from Euclid that I want to prove (see attachment). AD and EF lie on a line parallel to BC. I want to show that Area of ABCD = Area of BCFE. I believe to prove this I must first show that triangle ABE is congruent to triangle DCF (then show that triangle GBC = triangle...

I want to prove that the square of any integer is in the form of 4n or 4n + 1. I know that when we square any integer greater than 2 the result will be either divisible by four or four divides into the integer and leaves a remainder of one. How would I begin proving this in the most...

We are given that ABCD is a rectangle and AE is the diameter of the circle, and BFGH is a square. I want to figure out how to show that ABCD has the same area as BFGH. Where do I even begin? (see attached picture)

Yea it definitely doesn't prove that they are similar. I cannot use the pythagorean theorem to prove this. I must show that the both of the inscribed triangles are similar to ABC using the sides a, b, and c. I just have no clue on how to begin to show proportionality of the sides (I have...

Thank you so much for your help micro and Bahat. I was overlooking distributivity. Thank you and I have it solved now. Not sure how I go about marking a thread as solved. I will try and do it by editing the title of my main post.

CD is a perpendicular from C to AB. Prove that triangles ACD and CBD are both similar to triangle ABC. (See attached image) I can prove corresponding angles are congruent very easily for ABC and CBD. For example, angle A = angle A for both ABC and ACD. Also, angle D = angle C since ABC is...

I am struggling on how to manipulate k^2(k+1)^2/4 + (k+1)^3 to equal (k+1)^2(k+2)^2/4 If I get a common denominator I get I am struggling on how to manipulate (k^2(k+1)^24 + 4(k+1)^3)/4 However, I cannot find the route that leads to f(k+1).

I need to show that k^3 + \big( \frac{(k+1)(k+2)}{2} \big)^2 = (k + 1)^3 or am I way off on my induction basics? I am following the guide I found at wolfram here http://demonstrations.wolfram.com/ProofByInduction/ However, I cannot get the algebra to work out where f(n) + a_(n+1) = f(n+1)...

Solved: Is this an induction problem? (1+2+3+ \cdots + n)^2 = 1^3 + 2^3 + 3^3 + \cdots + n^3 , n \ge 1 Provide a derivation of the identity above. I do not know how to begin this problem. I tried to use induction but did not succeed. Also, I honestly do not know what it means by...