How would I prove that $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$ for any positive integer $n$?
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
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algebra-precalculus
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3Do you know the binomial theorem? – 2012-09-24
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0Hint: let $\:2 = x,\:$ so $\rm\:3 = 1+x.\:$ Recognize the famous theorem now? – 2012-09-24