Halo Posted September 8, 2012 Share Posted September 8, 2012 Hello These notes were taken from a lecture I had the other day: [math]\sum\limits_{k=0}^m \binom{m}{k}x^k + \sum\limits_{k=0}^m \binom{m}{k}x^{k+1}[/math] [math]= \sum\limits_{k=0}^m \binom{m}{k}x^k + \sum\limits_{k}^{m+k} \binom{m}{k}x^{k(k+1)}[/math] [math]= \binom{m}{0}x^0 + \sum\limits_{k=1}^m (\binom{m}{k} + \binom{m}{k-1})x^k + \binom{m}{m}x^{m+1}[/math] [math]= 1 + \sum\limits_{k=1}^m \binom{m+1}{k}x^k + x^{n+1}[/math] [math]= \sum\limits_{k=0}^{m+1} \binom{m+1}{k}x^k[/math] Can someone please explain to me by which rules these steps are possible, because it is all greek to me at the moment. The steps are part of a proof for the Binomial Theorem. Thanks in advance! Link to comment Share on other sites More sharing options...
mathematic Posted September 9, 2012 Share Posted September 9, 2012 The second term on the second line looks wrong. What is the summation variable? What are the limits? The exponent k(k+1) is wrong. Link to comment Share on other sites More sharing options...
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