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Ord function and convergent in Qp

  1. Nov 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Solve the following :

    a) Show that ordp((p^n)!)=1+p+p^2+p^3+....+p^(n-1)

    b)For which values of p does the following series converge in Qp?
    1)1+(15/7)+(15/7)^2+(15/7)^3+......
    2)1!+2!+3!+4!+....


    2. The attempt at a solution



    For a) I wanna to count how many terms of (p^n)! containing the factor p but I failed using my way.

    For b) 1) I tried to use the definition of convergent in Qp but when i got the geometric series then it is complicated to analyse p and 2) I have no idea

    Can someone help me ?? many thanks
     
  2. jcsd
  3. Nov 17, 2013 #2

    haruspex

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    How many terms have the factor p^n? The factor p^(n-1) but not p^n? ....
     
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