$$\sum_{n=0}^k\binom{k}{n}2^n$$ 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.
2026-04-06 07:06:36.1775459196
Summation of Binomial Coefficients with geometric series
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This is just the expansion of $(1+2)^k$, and the answer is $3^k$.