China
Africa
Explore chapters and articles related to this topic
The binomial series
Published in John Bird, Higher Engineering Mathematics, 2017
The binomial series or binomial theorem is a formula for raising a binomial expression to any power without lengthy multiplication. The general binomial expansion of (a + x)n is given by: (a+x)n=an+nan−1x+n(n−1)2!an−2x200+n(n−1)(n−2)3!an−3x300+...
The binomial series
Published in John Bird, Engineering Mathematics, 2017
The binomial series or binomial theorem is a formula for raising a binomial expression to any power without lengthy multiplication. The general binomial expansion of (a+x)n $ a\,{+}\,x)^{n} $ is given by: (a+x)n=an+nan-1x+n(n-1)2!an-2x2+n(n-1)(n-2)3!an-3x3+⋯+xn $$ \begin{aligned} (a + x)^{\boldsymbol{n}}&= \boldsymbol{a}^{\boldsymbol{n}} + \boldsymbol{na}^{\boldsymbol{n}-1}\boldsymbol{x} + \frac{\boldsymbol{n}(\boldsymbol{n} -1)}\mathbf{2! } \boldsymbol{a}^{\boldsymbol{n}-2}\boldsymbol{x}^\mathbf{2} \\&\quad + \frac{\boldsymbol{n}(\boldsymbol{n} - 1)(\boldsymbol{n} - 2)}\mathbf{3! } \boldsymbol{a}^{\boldsymbol{n} -\mathbf 3 } \boldsymbol{x}^\mathbf{3}\\&\quad +\cdots +\boldsymbol{x}^{\boldsymbol{n}} \end{aligned} $$
Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations
Published in Inverse Problems in Science and Engineering, 2018
Assume , then using the binomial theorem for both and (which for converges as ) and using that the negative binomial coefficient can be written as follows:
Proof-related reasoning in upper secondary school: characteristics of Swedish and Finnish textbooks
Published in International Journal of Mathematical Education in Science and Technology, 2021
Regarding combinatorics, there were subsections in the Swedish books addressing probability, the binomial theorem, and Pascal’s triangle. In such subsections, only materials and tasks involving combinatorial reasoning have been included.
M-Sweeps multi-target analysis of new category of adaptive schemes for detecting χ2-fluctuating targets
Published in Journal of Information and Telecommunication, 2020
With the aid of binomial theorem, the bracketed quantities can be expanded as a binomial of y. Following this procedure of expansion, Equation (18) can be rewritten as: