Covers set theory (integers, prime and rational numbers), algorithms (Euclidean, RSA encryption), theorems (Euler, Fermat, Chinese remainder), induction proofs (well-ordered sets, weak and strong induction), combinatorics (permutations, combinations, combinatorial proofs of the binomial theorem, Pascal's identity).
For further mathematical detail, including an explicit formula for the kth term of a binomial expansion, see binomial theorem.
Thus, factorial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is defined as equal to 1. Factorials are commonly encountered in the evaluation of permutations and combinations and in the coefficients of terms of binomial expansions (see binomial theorem).
This diagram is similar to Blaise Pascal's triangle (see binomial theorem), which was discovered independently later in the West.
Multinomial theorem, in algebra, a generalization of the binomial theorem to more than two variables.
For example, Sir Isaac Newton used his binomial theorem to calculate 16 decimal places quickly.
(Consider "About binomial theorem I'm teeming with a lot o' news/With many cheerful facts about the square of the hypotenuse").
Now, by the binomial theorem, and I might add, the same binomial theorem that allowed us to get these results, we can also write that this is what?
First-time Splash attendee ADITYA KRISHNAN took a math class on the binomial theorem.
In particular, the proof of the binomial theorem and the explanation of the method of finding square roots are of this character.
To establish these results, he introduced transformations among the variables of the problem, using a result equivalent to the binomial theorem for integral exponents.
