that's awesome...i figure my biggest problem in math is perspective, often i delude myself and make problems harder in my mind then they are in reality.
Taken your question literally the 2^n is not multiplied by anything.
Consider \(\displaystyle 2^n = (1+1)^n\) .........[edited ... to the corner] Now using the binomial expansion to \(\displaystyle (1+1)^n \) we get [MATH]2^n=(1+1)^n=\sum_{k=0}^n\left({n \choose k}1^{k}1^{n-k}\right)[/MATH] =[MATH]\sum_{k=0}^n\left({n \choose k}\right)[/MATH]
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