Hello. I have a problem with one task. The task is: Suppose that you playing the game. You have n moves. on each move you win the game with probability p. Your winning amount is equal to move number. For example if you win in first move your winning amount is 1, if you win in n move, your winning amount is equal to n, and if you not win, your winning amount is 0. Need to prove that average winning amount is: (1+n(1-p)^n+1-(n+1)(1-p)^n)/p My try: 1/n [itex]\sum[/itex] k*p(1-p)^k-1, for k=1 to n. And tryed to do something but nothing goes on. For example: 1/n(n*p*(1-p)^n-1+(n-1)*p*(1-p)^n-2+...+(n-n+1)*p*(1-p)n-n but cant get the right answer. Thanks for helping.