How can I simplify this summation?

[nightcrrawlerr]

Look, nightcrrawlerr. Could you pls. help me? I am not supposed to, nor do I want to, do your homework for you. What I've already posted is really close to doing that and I'm not going any farther. You have an expression and you have explicit instructions for a calculation that will complete it. If you don't know what a derivative is, then this problem was assigned by mistake and I would complain to your instructor.

Dick, I do appreciate your response to my post. Your answers and explanations.

You probably correct friend. Honestly I took this course twice already at first I drop this because I know I can't make it. For honest reason, I took this for the second time. Why? Because its part of my curriculum and I can't scape it.

Can I took "Algorithm and analysis" by just studying Discrete Math?

Since I don't really have any ideas of what a "Derivative" is, I have to read a lot of books just to understand what is this all about, right? But this is a study of algorithm and analysis and I supposed somebody could explain it well and help me in my comprehension so as through with this derivative.

With this, I understand I couldn't make it. I concede. This is not my cup of tea...

Again to those who help me out in this, thanks a lot.

To Dick, Mattson, slider142, cristo, dextercioby and to those who viewed this thread others who participated in here... thanks and more power.

May the grace our Lord Jesus be with you always.


Adios!

 

[Dick]

nightcrrawlerr,

I'm really sorry this has been so hard for you. I thought calculus at at least a basic level was required for a course like this. If not, then they are making a mistake including problems like this. I wish you luck in all your studies!

Dick

 

[Dick]

Therefore the initial sum is 2-1=1.

I'm SURE there is another way to do this. Because the infinite version of this series sums to 0.

 

[Dick]

Therefore the initial sum is 2-1=1.

Should read 2-2=0. That's the only problem. So there IS a way to do this without derivatives.

 

[Gib Z]

2\sum_{k=1}^{\infty}\frac{1}{2^{k}} =2 \left [\left(\sum_{k=0}^{\infty}\frac{1}{2^{k}}\right)-\left\frac{1}{2^{k}}\right|_{k=0} \right]=2(2-1)=2.

Quote dex: I hope this isn't the only way of solving this
I think u ment the entire solution, but for that summation here's a nice visual:

1x1 unit square. First term of series, 1/2, color in half the square. 2nd term, color in 1/4 of the remaining unshaded part. Then next term, 1/8, do the same. You'll see its going to fill it up. :D