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Category Archives: binomial coefficients
The Art of Proving Binomial Identities is Now Available
A couple of months ago I posted that my book, The Art of Proving Binomial Identities, would soon be finished. Well, it’s out now, and you can buy it straight from the publisher (CRC Press). It’s up on Amazon as well. … Continue reading
Posted in binomial coefficients, publishing
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Sum of the Reciprocals of the Binomial Coefficients
In this post we’re going to prove the following identity for the sum of the reciprocals of the numbers in column k of Pascal’s triangle, valid for integers : Identity 1: The standard way to prove Identity 1 is is … Continue reading
Posted in binomial coefficients, sequences and series
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The Art of Proving Binomial Identities
I recently finished a book, The Art of Proving Binomial Identities, that will be published by CRC Press later this year. We’re past the page proofs stage, and I think all that’s left on my end is to provide a little … Continue reading
Posted in binomial coefficients, publishing
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Equivalence of Two Binomial Sums
This month’s post entails proving the following equivalence: Identity 1: Despite the fact that these two sums are over the same range and are equal for all values of n they are not equal termbyterm. If you think about the two sides … Continue reading
Posted in binomial coefficients, probability
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A Sum of Ratios of Binomial Coefficients
In this post we evaluate the sum . Then we’ll generalize it and evaluate . The key tools we need for the first sum are the trinomial revision identity, , and the parallel summation identity, . Using trinomial revision, we have . … Continue reading
Posted in binomial coefficients
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