So I'm trying to prove that (n+1)/2 is the mean of the first n integers by math induction.
I mainly need help setting it up. Would it be:
(1+2+3+...+n)/n = (n+1)/2 ?
Good attempt, but not quite.
After your assumption that the statement is true for i, you need to prove it is true for (i+1).
That is, you need to prove that $\displaystyle \frac{1+2+3+...+i+(i+1)}{i+1} = \frac{(i+1)+1}{2}$
Have another go.
Also, another point:
With a proof like this, you should
(a) Work with the LHS only and turn it into the RHS.
OR (b) Work with the RHS only and turn it into the RHS.
OR (c) Work with the LHS as far as you can. Then work with the RHS as far as you can. Hopefully they will then be equal.
You can't work with both at the same time (as you've done) because you don't know at the beginning (yet) that the LHS=RHS.