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Second Weighted Sum
## Formula
$$\sum_{r=0}^{n}r(r-1){}^nC_r=n(n-1)2^{n-2}$$
Also:
$$\sum_{r=0}^{n}r^2{}^nC_r=n(n+1)2^{n-2}$$
## Usage
- Used in summations involving squares of the index multiplied by binomial coefficients.
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Second Weighted Sum
## Formula
$$\sum_{r=0}^{n}r(r-1){}^nC_r=n(n-1)2^{n-2}$$
Also:
$$\sum_{r=0}^{n}r^2{}^nC_r=n(n+1)2^{n-2}$$
## Usage
- Used in summations involving squares of the index multiplied by binomial coefficients.
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