The series which arises in the binomial theorem for negative integer -n ,. (x+a)^(-n), = sum_(k=0)^(infty)(-n; k). (1). = sum_(k=0)^(infty)(-1)^k.

The binomial theorem for positive integer exponents n can be generalized to negative integer exponents. This gives rise to several familiar Maclaurin series ...

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a ...

Negative Binomial Series. The Series which arises in the Binomial Theorem for Negative integral $n$ ,. $\displaystyle (x+a)^{-n}$, $\textstyle = ...

... negative binomial series defined by the MacLaurin series for ... The negative binomial series includes the case of the geometric series, the power series ... Summation of the binomial... · Negative binomial series

26 нояб. 2011 г. · Negative Exponents in Binomial Theorem · The first sum only converges if |ab|>1 whereas the second sum only converges if this is less than 1, so ... Understanding why binomial expansions for negative integers ... Negative Binomial Series - Math Stack Exchange Intuitive explanation for negative binomial expansion Why does Negative binomial expansion have infinite terms Другие результаты с сайта math.stackexchange.com

In 1676 Newton showed that the binomial theorem also holds for negative integers n, which is the so-called negative binomial series and converges for |x| < y.

In this explainer, we will learn how to use the binomial expansion to expand binomials with negative and fractional exponents.

Продолжительность: 9:40
Опубликовано: 3 окт. 2021 г.