Can you do binomial expansion with negative power?
Can you do binomial expansion with negative power?
The binomial theorem for positive integer exponents n can be generalized to negative integer exponents. This gives rise to several familiar Maclaurin series with numerous applications in calculus and other areas of mathematics.
Can a binomial term be negative?
The term “negative binomial” is likely due to the fact that a certain binomial coefficient that appears in the formula for the probability mass function of the distribution can be written more simply with negative numbers.
What is r in negative binomial?
The negative binomial random variable is R, the number of successes before the binomial experiment results in k failures. The mean of R is: μR = kP/Q. The negative binomial random variable is K, the number of failures before the binomial experiment results in r successes.
What is the factorial of negative numbers?
The factorials of real negative integers have their imaginary part equal to zero, thus are real numbers. Similarly, the factorials of imaginary numbers are complex numbers. The moduli of the complex factorials of real negative numbers, and imaginary numbers are equal to their respective real positive number factorials.
Can PMF be negative?
Yes, they can be negative Consider the following game. If we let X denote the (possibly negative) winnings of the player, what is the probability mass function of X? (X can take any of the values -3;-2;-1; 0; 1; 2; 3.)
Can A binomial expression be expanded for a negative integer?
I understand how a binomial expression can be expanded for positive integer indices by using pascals triangle or combinations to find out the number of ways different terms occur. However, I do not understand why the same logic can be used with negative and fractional powers.
Is the negative binomial theorem relevant to calculus?
Relevant For… n n can be generalized to negative integer exponents. This gives rise to several familiar Maclaurin series with numerous applications in calculus and other areas of mathematics. f (x) = (1+x)^ {-3} f (x) = (1+x)−3 is not a polynomial. While positive powers of f (x) f (x).
Which is the binomial series for positive exponents?
The binomial series for positive exponents gives rise to a nite number of terms ( n+ 1 in fact if n is the exponent) and in its most general form is written as: (x + y)n = P. n k=0 nx ky .
Why does the expansion of binomial theorem give infinite terms?
When, ‘ $ n $’ is negative and/or fractional number , then the expansion of binomial theorem always gives infinite terms because there are infinite number of possibilities of $a^pb^q$ such that p+q=n and $ q $ is always a positive number.
