Difference between revisions of "Binomial theorem"
From specialfunctionswiki
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The following formula holds: | The following formula holds: | ||
$$(a+b)^n = \displaystyle\sum_{k=0}^n {n \choose k} a^k b^{n-k},$$ | $$(a+b)^n = \displaystyle\sum_{k=0}^n {n \choose k} a^k b^{n-k},$$ | ||
| − | where ${n \choose k}$ denotes the [[binomial coefficient]] | + | where $\displaystyle{n \choose k}$ denotes the [[binomial coefficient]] |
==Proof== | ==Proof== | ||
Revision as of 18:04, 25 September 2016
Theorem
The following formula holds: $$(a+b)^n = \displaystyle\sum_{k=0}^n {n \choose k} a^k b^{n-k},$$ where $\displaystyle{n \choose k}$ denotes the binomial coefficient
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (next): 3.1.1
