Recent content by aeonsky

I don't think I am quite looking for that. I need to find the sum of all odd integers between 1 and odd integer n. Thus, if you need to find (3), the sum will be 4. (5), the sum will be 9. (7), the sum will be 16. I found the formula (N+1)(N+1)/4 where n is the odd integer, but not the...

\sum_{i=1}^{n} i is the sum of all numbers between 1 and n. I'm trying to find one for odd numbers where you need to find the sum of all odd numbers between 1 and n. I tried 2n+1 which worked, only for first n numbers, not for numbers 1 to n. Thanks for the help.

Oh, haha, Mark you were right. It is valid for every solution (I didn't read your reponse correctly). Thanks. You too union.

I forgot about this part (quote from my book): "...to disprove a general rule, all we need is one counterexample. On the other hand, to prove a general rule is more difficult, we must prove it for all cases, which we usually do by algebraically providing an arbitrary typical case with letter...

Ok, I will look that up. I was just a little suspicious since there are about 40 problems that require you to do the same for different rules and all solutions to odd exercises had counterexamples. Thanks.

But aren't there infinitely many solutions for that equation? If I come up with 1 or 2 random solutions to the equations, and prove all 10 axioms with them, that doesn't necessarily mean that the next 1 or 2 random solutions will be not counterexamples. Am I wrong? I say 1 or 2 because some...

Homework Statement Does this set describe a vector space? Te set of all solutions (x,y) of the equation 2x + 3y = 0 with addition and multiplication by scalars defined as in R^2.Homework EquationsAssociativity of addition u + (v + w) = (u + v) + w. Commutativity of addition v + w = w + v...

Homework Statement Evaluate the indefinite integral... \int x^2 (x^3+5)^9 dx Homework Equations \int f(g(x))g'(x)dx = \int f(u)du The Attempt at a Solution u = x^3+5 du = x^2dx So my answer is... Does that look right? And one more... Homework Statement Evaluate the indefinite...

I need to find the derivative of the function below... Homework Statement G(x) = \int_{x}^{1} cos(\sqrt{t}) dt Homework Equations FTC1 If f is continuous on [a,b], then the function g defined by g(x) = \int_{a}^{x} f(t) dt a \leq x \leq b is continuous on [a,b] and differentiable on...