Recent content by venom192

  1. V

    Finding Alternative Representations for the Convergent Series Ʃ ((-1)^(i-1))/i

    Thanks for the reply. This question specifically pertains to the series I asked about - I was just using the Taylor series as a possibility of an alternate representation of the series. After looking at my old calc textbook, I see that I was way off base suggesting a Taylor series. I'll...
  2. V

    Graduate Power Series Expansion: Find Alternatives to Ʃ ((-1)^(i-1))/i

    I posted this in the homework section, but it's not a homework problem. I basically need to know if the series Ʃ ((-1)^(i-1))/i can be represented in other ways (e.g. a Taylor series, but I doubt it). I know it converges to ln2, but I need to know if there's a series like x^2, x^4, ... or...
    • venom192
    • Thread
    • Expansion Power Power series Series Series expansion
    • Replies: 1
    • Forum: Calculus
  3. V

    Can a Set of 5 Vectors Span All of R6?

    How many vectors span R2? R3?
  4. V

    Finding Alternative Representations for the Convergent Series Ʃ ((-1)^(i-1))/i

    Homework Statement I basically need to know if the series Ʃ ((-1)^(i-1))/i can be represented in other ways (e.g. a Taylor series, but I doubt it). I know it converges to ln2, but I need to know if there's a series like x^2, x^4, ... or something like it that I can represent the series...
  5. V

    Matrix Vector Spaces: Invertible Basis?

    Homework Statement Does the vector space of all square matrices have a basis of invertible matrices? Homework Equations No relevant equations. The Attempt at a Solution I know that the 2x2 case has an invertible basis, but I don't know how to generalize it for the vector space...