mean for the amount of money won for flipping a coin n times and winning m dollars on the m-th flip if it is tails I am flipping a coin n times. if it lands on heads, i win nothing but if it lands on tails on the m-th flip, i get m dollars. how much money can i expect to you at the end of the game. 
I looked at each coin flip on the m-th try. For example,
using the mean of a random variable formula where mu = n*p
1st coin flip -> .5 chance of winning .50 dollar
2nd coin flip -> .5 chance of winning 1 dollar
3rd coin flip -> .5 chance of winning 1.5 dollars
4th coin flip -> .5 chance of winning 2 dollars
ect.
For the example above, I can expect to win 5 dollars which is just the sum of the m-th flip divided 2. so in our example, I would expect to earn 10/2 dollars
so by the end of the game I should expect to win (m1+m2+m3+....+mn)/2 dollars.
Is that correct or am I supposed to get a solid number, and not in terms of variables.
Any help would be appreciated.

You seem to be pretty much spot on.
Keep in mind that $1+2+3+4+...+x-1+x=x(x+1)/2$
This means that you can solve for an equation for your winnings dependant only on n (the number of flips). Without a value of n or a new rule (like the one suggested below) there is no way to get a solid number.
This all assumes that every times you flip the coin and it lands on tails you win and can keep playing until your nth flip.  It might be a more interesting problem if you stop after it lands on tails. This would give you an exact number.
