The problem statement, all variables and given/known data Prove the binomial theorem by induction. The attempt at a solution http://desmond.imageshack.us/Himg35/scaled.php?server=35&filename=sumu.png&res=landing [Broken] Hi, running into trouble with this proof and google hasn't helped me. I don't understand the jump here, and as it's not really explained in the videos/.pdf's I found I presume it's something really simple that I'm just not getting. I saw one explanation saying "just put k=j+1, put k in the equation in place of j then switch back to j" and while it worked I'm not seeing why I can replace j with k, as k=/= j. Any input would be appreciated, this is really puzzling me.