The Purplemath Forums

In one of my math problems the answer stated that going from n^2 to 2n^2 is an increase by a factor of 4. I dont understand how this is. Can someone explain?

Thanks alot. I thought about this last night and came to the same conclusion that I was "assuming" that the equation was like this 2(n^2) vs (2n)^2. Thanks!

For the following problem: 2-2*7 + 2 * 7^2 - … + 2* (-7)^n = (1-(-7)^n+1)/4 I understand that I need to first solve this for P(0). What I dont understand is how the left side of the equation is equal to 2. Maybe I'm messing up the sequence of the equation or something but when I do the math I get: (...

The problem: 2-2*7 + 2 * 7^2 - … + 2* (-7)^n = (1-(-7)^n+1)/4 is to be proved P(n). I already know the answer to the problem. What I am trying to do is figure out how it was found. Here is a snipped for the answer: "In order to prove this for all integers n>= 0, we first prove the base case P(0...

All, Looking for some help in factoring the following equation: (k(k+1)(2k+1))/6 + (k+1)^2 I have gotten this far: (k(k+1)(2k+1)+6(k+1)^2)/6 I was checking the exponent rules and got the following for 6(k+1)^2: 6k^2 but I ran the same equation through the mathway solver and got 6k^2 + 12k + 6. I che...