Question on writing summations in expanded form

  1. Hello everyone.

    I have the following:

    THe sumnation of 1/k! from k = 0, to n. I"m suppose to write this in expanded form.

    I did the following:
    1/0! + 1/1! + 1/2! + 1/3! +....+1/n! = 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 +...+ 1/n!

    Is that what they wanted?
    An example simliar to this one was the following:
    Sumnation (-2)^i from i = 1 to n.
    (-2)^1 + (-2)^2 + (-2)^3 + ... + (-2)^n = -2 + 2^2 -2^3 +...+(-1)^n(2)^n

    from mine the signs don't seem to be changing, so is it just simply 1/n!

    Also i was wondering if someone could check to see if i did this one correctly:
    Write each using summnation or product notation.

    41. n + (n-1)/2! + (n-2)/3! + (n-3)/4! + .. + 1/n!

    I said:
    Sumnation from k = 1 to n, (n-k)/n!


    Thanks!
     
    Last edited: Sep 25, 2006
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,939
    Staff Emeritus
    Science Advisor

    Yes, that is correct.

    Not quite. n is a fixed number, k is changing so the denominator is not n!, it is k!.
     
  4. Thanks for the help!
     
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