Recent content by Aspiring

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    Graduate Is the Taylor Series Method Valid for Proving the Irrationality of ln(π)?

    Aw of course, i see now, thanks.
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    Graduate Is the Taylor Series Method Valid for Proving the Irrationality of ln(π)?

    If we set out to prove the irrationality of the natural logarithm of π (pie), by writing out the Taylor series centered at zero for the function y=π^x, with x=1, we have: π=1+Sum(ln^k(π)/k!) from k=1 to infinity. Since we know π is irrational, then ln(π) must be irrational or otherwise...
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    Graduate How can I generalize the derivative of a reciprocal function?

    Yes exactly! just k'(x) is not specified! Surely it must be possible to find an nth derivative formula using the quotient rule?
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    Graduate How can I generalize the derivative of a reciprocal function?

    Okay, let me clarify. I wish to find a formula that will give me the nth derivative of the reciprocal of κ'[x]. Just as the the nth derivative of the function e^ax is given by a^n(e^ax); I'am looking for the equivalent with the above function. Whether the function for the nth derivative is...
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    Graduate How can I generalize the derivative of a reciprocal function?

    Not Quite; just a function that when I enter, say n=1 , as its argument it results in it's first derivative and so on. I don't want to calculate the function at points or find a power/Taylor series representation. I have tried to generalize but I can't find a pattern, using the quotient rule to...
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    Graduate How can I generalize the derivative of a reciprocal function?

    Hi guys, I need help generalizing the derivative of the reciprocal of the function μ'(×). What I would to find is a series representation whereby I don't have to find any derivatives of the function but merely replace powers and orders of derivatives. Leibniz's series expression for the...