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Posers and Puzzles

Posers and Puzzles

  1. Standard member genius
    Wayward Soul
    21 May '04 15:54 / 2 edits
    prove by induction that ((d^n)/(d(x^n)))/(x(e^x))=(x+n)(e^x) for all integers n>=1.

    (incase you're sondering-this is the other part of my paper i couldn't get...however, i have recently discovered that i have got it right...apparently... tis a 5-marker...)
  2. 21 May '04 22:21
    Originally posted by genius
    prove by induction that ((d^n)/(d(x^n)))/(x(e^x))=(x+n)(e^x) for all integers n>=1.

    (incase you're sondering-this is the other part of my paper i couldn't get...however, i have recently discovered that i have got it right...apparently... tis a 5-marker...)
    Well a general law for a quiz type thread is that the originator knows the answer to the question. Since you confirmed to us that you got it right. I induce that it must be proven.
  3. Standard member TheMaster37
    Kupikupopo!
    22 May '04 11:38
    Originally posted by genius
    prove by induction that ((d^n)/(d(x^n)))/(x(e^x))=(x+n)(e^x) for all integers n>=1.

    (incase you're sondering-this is the other part of my paper i couldn't get...however, i have recently discovered that i have got it right...apparently... tis a 5-marker...)
    I suppose that you mean the n-th derivative to x, and you typed a '/' too many?? I will write E for e^x and D for derivative or d/dx

    D^n (xE) = (x+n)E

    Case n=1: D^1 (xE) = xE + E = (x+1)E, correct

    INDUCTION STEP: Suppose the statement is correct for n=k, then D^(k+1) (xE) = D^1 ( D^k (xE)) = D^1 ((x+k)E) = (x+k)E + E = (x+k+1)E, correct

    Thus the given statement is correct for all integers n >= 1