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Fungrim entry: 081188

(z+1k+1)=(zk)+(zk+1){z + 1 \choose k + 1} = {z \choose k} + {z \choose k + 1}
Assumptions:z∈C  and⁡  k∈Z≥0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
TeX:
{z + 1 \choose k + 1} = {z \choose k} + {z \choose k + 1}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Binomial(nk){n \choose k} Binomial coefficient
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("081188"),
    Formula(Equal(Binomial(Add(z, 1), Add(k, 1)), Add(Binomial(z, k), Binomial(z, Add(k, 1))))),
    Variables(z, k),
    Assumptions(And(Element(z, CC), Element(k, ZZGreaterEqual(0)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC