1. The problem statement, all variables and given/known data (1/2!)+(2/3!)+(3/4!)+.....+(n/(n+1)!) a) calculate for a few small values of n. b) Make a conjecture about a formula for this expression c)Prove your conjecture by mathematical induction. 2. Relevant equations 3. The attempt at a solution So for the first part I just used values n=1,2,3 so.. n=1 1/2!=1/2 n=2 2/3! = 1/6+1/2 n=3 3/4! = 1/8+1/6+1/2. for part b) make a conjecture about the formula It should be ((n+1)!-1)/(n+1)! for part c) I am getting stuck... test for n=1, which is true assume true for n=k show true for n=k+1 so.... (1/2!)+(2/3!+(3/4!)+....+(k/(k+1)!)+((k+1)/(k+2)!) = ((k+2)!-1)/(k+2)! where (1/2!)+(2/3!+(3/4!)+....+(k/(k+1)!)= ((k+1)!-1)/(k+1)! so... ((k+1)!-1)/(k+1)!+(k+1)/(k+2)!= ((k+2)!-1)/(k+2)! but Im lost as to where to go from here, have I made a mistake??? Help!