Recent content by theRukus

  1. T

    Big-Oh Notation

    Homework Statement Determine the complexity of the following code: for (i = 0; i < 2*n; i += 2) { for (j=n; j > i; j--) { a++; } } The Attempt at a Solution Well.. The first for block is O( n ) because i is incremented by 2 each loop up to 2n. The second block...
  2. T

    Combinatorics Class - Sum Question

    Or will it be \sum\limits^n_{i=0} \dfrac{\dbinom{n}{i}}{n!} I'm confused as to whether the sum is still involved.
  3. T

    Combinatorics Class - Sum Question

    So the answer I'm looking for is \frac{\dbinom{n}{i}}{n!} Correct?
  4. T

    Combinatorics Class - Sum Question

    Homework Statement For any positive integer n determine: \sum\limits^n_{i=0} \frac{1}{i!(n-i)!} Homework Equations I don't really know where to start.. Up until this point we've just been doing permutations, combinations, and determining the coefficient of a certain term in the expansion of...
  5. T

    Sum of Series

    Ah, perfect. I love you guys, you're so helpful. I guess I need to be a little more critical of my own work though, before I give up on what I've done completely. Now though, knowing A & B (I guess I was solving for them wrong), I am still confused as to how to get the 'nth term' of a series...
  6. T

    Sum of Series

    Alright, well this is what I've done: \frac{6}{n(n+1)} = \frac{A}{n} + \frac{B}{n+1} \frac{6}{n(n+1)} = \frac{A(n+1) + Bn}{n(n+1)} 6 = A(n+1) + Bn 6 = An + A + Bn Split into two equations, 1: 6 = A + B 2: 6 = A Then, 2->1: 6 = 6 + B B = 0 I can see I'm doing something wrong, because...
  7. T

    Sum of Series

    Alright, I've separated the equation into the following: \frac{6}{n(n+1)} = \frac{A}{n} + \frac{B}{n+1} And solved for A, B, getting A = 6, B = 0. So, I'm left with: \sum\limits^\infty_{n=1} \frac{6}{n} Now, I'm lost as to what to do. I don't know how to solve for this sum... Any hints...
  8. T

    Sum of Series

    Homework Statement Evaluate the sum of the following: \sum\limits^\inf_{n=1} \frac{6}{n(n+1)} Homework Equations The Attempt at a Solution Well... The denominator is going to get infinitely large as n approaches infinity, so would the value of the sum not converge to zero? The...
  9. T

    Comparison Test: Am I using a good comparison function?

    Homework Statement Does the following interval diverge? \int^9_1 \frac{-4}{\sqrt[3]{x-9}} Homework Equations The Attempt at a Solution Well.. I've used the following function that I think is always less than the above function to prove that the function above DOES NOT diverge (by...
  10. T

    Partial Frac. Decomp. Integral ( long div? )

    Got it! Thanks guys, I owe an infinite amount of thanks to PhysicsForums..!
  11. T

    Partial Frac. Decomp. Integral ( long div? )

    Homework Statement \int^1_0 \frac{-3x^3+12x+30}{x^2-x-6}dx Homework Equations The Attempt at a Solution I've attempted long division, but the long division does not seem to come to an end.. I'm not sure what to make of this.. If the long division does not end, does this mean that...
  12. T

    Integral (Partial-Frac Decomp) SIMPLE?

    Integral (Partial-Frac Decomp) **SIMPLE? Homework Statement \int^3_2 \frac{-dx}{x^2-1} Homework Equations The Attempt at a Solution = \int^3_2 \frac{A}{x} + \frac{B}{x-1} dx For some integers A and B. -1 = A(x-1) + B(x+0) -1 = Ax - A + Bx Split into two equations...
  13. T

    Trig Identity Integral

    Homework Statement I missed one class on trigonometric identities in integrals, and I feel that one is needed here: \int^3_0\frac{1+arctan(\frac{x}{3})}{9+x^2}dx Homework Equations The Attempt at a Solution Again, I'm unsure what to do. I think that it is a trig identity, but I could be...
  14. T

    Derivative of an Integral

    So the answer would be, -\frac{sin(x^2)}{x^2} \cdot 2x Is this now correct?
  15. T

    Derivative of an Integral

    Homework Statement Find the derivative of the function F(x) = \int^0_{x^2-1}\frac{sin(t+1)}{t+1}dt Homework Equations The Attempt at a Solution F'(x) = -\frac{sin(x^2)}{x^2} I'm just learning this and unsure if this is correct. It seems too easy?
Top