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$$\sum_{n=0}^k\binom{k}{n}2^n$$ Hi Im trying to prove an identity with this sum being a key feature, I was wondering if there was a direct formula for the sum of this product. I know the sums for each of the products individually but not together.

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  • $\begingroup$ Usually, $n$ and $k$ are reversed. $\endgroup$
    – RobPratt
    Commented Oct 19, 2020 at 21:22

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This is just the expansion of $(1+2)^k$, and the answer is $3^k$.

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