I see at least four difficulties in your code:
a) You shouldn’t use the word ‘sum’ for a variable. Matlab has a function by that name and this function expects an argument. Use some other name.
b) The series you describe does not converge to e. Probably it is 1/k! = 1/factorial(k) that you are thinking of.
c) The variable ‘answer’ remains at a constant value of 1, not e, so your while loop would never stop, (once you correct the above a) error.)
d) In the line:
the variable 'term' would not be the next term but would be the partial sum and therefore the next line would be totally incorrect:
It would amount to calculating the cumulative sum of partial sums - something you certainly don't want. Correction: No, it would actually amount to a kind of doubling of partial sums at each step. It would very soon overflow matlab's maximum possible numerical value, 'realmax', which is a terrifically large number.
Addendum: The sum of the infinite series 1/k^2 would actually give you pi^2/6. To show this, look up the definition of the first Bernoulli number, B1, and its value.
