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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∈{0,1,…n}z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \{0, 1, \ldots n\}
TeX:
{z + 1 \choose k + 1} = {z \choose k} + {z \choose k + 1}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \{0, 1, \ldots n\}
Definitions:
Fungrim symbol Notation Short description
Binomial(nk){n \choose k} Binomial coefficient
CCC\mathbb{C} Complex numbers
ZZBetween{a,a+1,…b}\{a, a + 1, \ldots b\} Integers between a and b inclusive
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, ZZBetween(0, n)))))

Topics using this entry

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

2019-06-18 07:49:59.356594 UTC