Cannot get my head around these functions - guidance needed please

Hi everyone, I'm normally ok with algebra, functions and the like but this question was posed in a clicker question in class and I don't know how to approach answering it.

The following functions produce the same answer, true or false?

f(n) = if n=0 then 1, else n + f(n-1)

g(n) = n(n+1)/2

As I have stated, this question formed part of a clicker question is class - but I would like to know the steps to solving it should something similar pop up again. The question takes a max of 3 mins to answer (clicker question limit) so I don't imagine a long rambling solution is required. As I say, any steps in solving this bad boy would be appreciated.

Re: Cannot get my head around these functions - guidance needed please

g(0) = 0, but f(0) = 1, so these are different functions.

On the other hand, if we had

then

The second last equality is the sum of an arithmetic progression.

Re: Cannot get my head around these functions - guidance needed please

Did it not ever occur to you to actually evaluate g(0)?