Binomial theorem: Difference between revisions

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In [[elementary algebra]], the '''binomial theorem''' is the identity that states that for any non-negative [[integer]] ''n'',
In [[elementary algebra]], the '''binomial theorem''' is the identity that states that for any non-negative [[integer]] ''n'',


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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''&nbsp;+&nbsp;''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''&nbsp;+&nbsp;''y'')<sup>''n''</sup> as an infinite series when ''n'' is not an integer or is not positive.
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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.