How can I calculate the following sum involving binomial terms: ∑k=0n(nk)(−1)k(k+1)2
How can I calculate the following sum involving binomial terms:
Answer & Explanation
Beginner2022-01-25Added 9 answers
Setting gives an expression for your sum,
Now, , so
Beginner2022-01-26Added 15 answers
One application of the absorption identity gets one of the factors of out of the denominator:
By using the basic binomial coefficient recursion formula, we can make that happen.
Let Then looking at the difference of and gives us
where in the last step we used the fact that the alternating sum of the binomial coefficients is 0.
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