Ord function and convergent in Qp

[Funky1981]

Homework Statement

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 want to 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

 

[haruspex]

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

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