for k in range(len(word)): 
    print word[ :1+k]

n = int(raw_input('How many terms? ')) 
e = 0.0 
for k in range(n):
    # compute factorial for k as above
    factorial = 1
    for val in range(2,k+1):   # up to but not including k+1
        factorial *= val
    # now add in a new term
    e += 1.0/factorial         # note use of float 1.0 in numerator

We can do even better by not recomputing the factorial from scratch each time, but instead basing it on the previous iteration, as follows.

e = 1.0         # let's add in first term by hand for 1/0!
factorial = 1
for k in range(1,n):   # other n-1 terms
    # update factorial
    factorial *= k
    # add new term
    e += 1.0/factorial         # note use of float 1.0 in numerator

In either case, the approximation that is computed using only the first 10 terms is 2.71828152557. (That's pretty good, as the actual value of e starts with 2.718281...)

original = raw_input('Enter numeric string: ')
base = int(raw_input('What base is the number? '))
place = 1               # we will start with the one's digit
total = 0
original = original[ : :-1]   # reverse for convenience
for symbol in original:
    total += int(symbol) * place
    place *= base             # next column is worth "base" times more than previous
print total

Python does not offer any formal guarantee as to the semantics of looping over a sequence as it is mutated, and the observed behavior might vary from version to version of Python. That said, on our current system we observe the output:

A 
C 
E 
A 
E 
E