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Who has anything new to say about the binomial theorem at this late date?
The power set is closely related to the binomial theorem.
Applying the binomial theorem which states we can reduce to:
Several theorems related to the triangle were known, including the binomial theorem.
It is the generalization of the binomial theorem to polynomials.
Using the Binomial theorem to second order it follows:
Briggs discovered, in a somewhat concealed form and without proof, the binomial theorem.
A less laborious way of achieving the same result is by using the generalized binomial theorem.
He wrote on the binomial theorem and Pascal's triangle.
The binomial theorem can be generalised to include powers of sums with more than two terms.
For larger positive integer values of n, the correct result is given by the binomial theorem.
This approximation can be obtained by using the binomial theorem and ignoring the terms beyond the first two.
At the age of twenty-one he wrote a treatise upon the binomial theorem, which has had a European vogue.
It is not difficult to turn this argument into a proof (by mathematical induction) of the binomial theorem.
The binomial theorem can be applied to the powers of any binomial.
Induction yields another proof of the binomial theorem (1).
He also created the binomial theorem, worked extensively on optics, and created a law of cooling.
Algebraic manipulations (in particular the binomial theorem) are avoided.
The binomial theorem also holds for two commuting elements of a Banach algebra.
See also binomial coefficient and the formally quite similar binomial theorem.
An interesting consequence of the binomial theorem is obtained by setting both variables x and y equal to one.
The binomial series is therefore sometimes referred to as Newton's binomial theorem.
- it's binomial theorem on the line.
He used it to prove the binomial theorem, Pascal's triangle, and the sum of integral cubes.
Newton is generally credited with the generalised binomial theorem, valid for any exponent.