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Series question t/f

  1. Apr 6, 2009 #1
    True/false The taylor series below converges for all x to e^-x

    n-infinity
    [tex]\sum[/tex] (-1)^(n-1) * 1/n * x^n
    n=1
     
  2. jcsd
  3. Apr 6, 2009 #2
    well the series for e^x is Sum: x^n/n!

    I will assume you forgot to put the factorial in there. Cause then it is obviously falso

    So now (-1x)^n/n!= (-1)^n x^n/n! = e^-x

    So this is false, it converges to -e^-x

    my notaion is very sloppy, but you get the picture
     
  4. Apr 6, 2009 #3
    nope did not forgot the factorial. Why is it obviously false then.
     
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