Binomial theorem: Difference between revisions
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== The first several cases == | == The first several cases == | ||
<math> \begin{align} | |||
(x + y)^0 &= 1 \\ | (x + y)^0 &= 1 \\ | ||
(x + y)^1 &= x + y \\ | (x + y)^1 &= x + y \\ | ||
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There is also '''Newton's binomial theorem''', proved by [[Isaac Newton]], that goes beyond elementary algebra into mathematical analysis, which expands the same sum (''x'' + ''y'')<sup>''n''</sup> as an infinite series when ''n'' is not an integer or is not positive. | There is also '''Newton's binomial theorem''', proved by [[Isaac Newton]], that goes beyond elementary algebra into mathematical analysis, which expands the same sum (''x'' + ''y'')<sup>''n''</sup> as an infinite series when ''n'' is not an integer or is not positive. | ||
Revision as of 16:24, 15 July 2008
In elementary algebra, the binomial theorem is the identity that states that for any non-negative integer n,
or, equivalently,
where
One way to prove this identity is by mathematical induction.
The first several cases
Newton's binomial theorem
There is also Newton's binomial theorem, proved by Isaac Newton, that goes beyond elementary algebra into mathematical analysis, which expands the same sum (x + y)n as an infinite series when n is not an integer or is not positive.