Recent content by PhysicsBoyMan

Sorry, its (k / (2k + 1)) + (1 / ((2k)(2k+2))

(k / 2k + 1) + (1 / (2k)(2k+2)) = ((k+1) / (2k+2)) I would like to simplify the left side to prove that these two statements are equal. I'm not sure how to do this. Surely I can't find a common denominator with such complex variables and such? What is a good approach?

d Nice one Perok. Contradictions are a lot more intuitive often times.

Thanks. I didn't think about it like that. That is, starting with a separate true statement and transforming it into the one I want.

How is that a proof that 2ab is always less than or equal to a2 + b2 when a and b are integers?

I don't know what some of your comment means. I'm trying hard to figure it out. I'm looking at the term (a-b)2 and I think that may be the "certain square" you are talking about. It's equal to a2 + b2 - 2ab though so I don't know what I could substitute it for. Maybe I'm on the wrong track here...

Well I know that squares are always positive.

a and b are integers Prove that: 2ab <= a2 + b2 I have tested various values for a and b and determined that the statement seems to be generally true. I'm having a hard time though constructing a formal proof. It will not do to suppose the statement is wrong and then provide a counterexample...

How would you know if a difficult statement like 3(2k+1)3 can be divided by 2

I have the answer. 3 times any odd makes an even, but the third power of that even is always odd.

3(2k+1)3 I have written a program which calculates the value of that polynomial with different values of k. The result is always an odd number. I am having a difficult time writing a proof that states that this polynomial always returns an odd number. I know that (2k + 1) is the general form...

I figured it out. I found the voltage reduction by each battery by going 0.6 amps x resistance value for battery. Then I took 3.6 V combined total from both batteries, subtracted both of the hits the voltage takes from the batteries that I calculated before, and I had the voltage for the lamp...

I forgot to add that the batteries have 1.8 V of electric potential each. Does anyone have any clues? I'm clueless and would really like to learn how to do this kind of problem.

The question is "What is the lamp's resistance" just to be clear.

Here is my updated sketch to match the feedback from you guys. With electric potential completely unknown, and resistance of the system only partially solved, I have no idea how to find RL AKA the lamp's resistance. Can someone point me in the right direction, maybe what to solve for first...