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Is it possible to derive a formula for this series? If there is, how can it be derived?

$$\sum_{R=1}^{K-1} (R\times2^R)$$

Wolgwang
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john li
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    There are multiple ways to do it. What have you tried? – DatBoi Nov 04 '20 at 16:07
  • Or perhaps https://math.stackexchange.com/questions/120091/how-do-we-get-the-result-of-the-summation-sum-limits-k-1n-k-cdot-2k and https://math.stackexchange.com/questions/11464/how-to-compute-the-formula-sum-limits-r-1d-r-cdot-2r? – player3236 Nov 04 '20 at 16:18
  • Thank you! I figured out the solution – john li Nov 04 '20 at 16:26

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Hint:

$$x\frac{d}{dx}\left(\sum_{n=0}^Nx^n\right)=\sum_{n=0}^Nnx^n$$

cansomeonehelpmeout
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