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Sum of the infinite series ((-1)^n * (-7)^n)/n!

  1. May 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the sum of infinite the series (-1)^n * 7^n/n! for n=1 to infinity

    2. Relevant equations

    e^x = sum (x^n)/n! for n=0 to infinity

    3. The attempt at a solution

    I combined the (-1)^n and the 7^n to make the summation ((-7)^n)/n! for n = 1 to infinity

    then I changed the lower bound to 0 to make it similar to e^x

    ((-7)^(n+1))/(n+1)! for n=0 to infinity

    I don't know where to go from here, help would be appreciated!
     
  2. jcsd
  3. May 14, 2012 #2

    tiny-tim

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    Welcome to PF!

    Hi Erubus! Welcome to PF! :smile:

    (try using the "Quick symbols" box, and the X2 button just above the Reply box :wink:)
    instead of changing the limits, just add a "0th" term …

    -1 + ∑0 (-7)n/n! :wink:
     
  4. May 14, 2012 #3
    Wow never would have thought of that, but it makes sense.

    Thanks!
     
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