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What is the newton's generalised binomial theorem?
Newton's generalized binomial theorem states that for any real number x and any real number r, the binomial expansion of (1 + x)^r converges if |x| < 1. The formula for the expansion is given by (1 + x)^r = 1 + rx + r(r-1)x^2/2! + r(r-1)(r-2)x^3/3! + ... + r(r-1)(r-2)...(r-n+1)x^n/n! for non-negative integer n.
What is the unit for the Universal Law of Gravity?
The unit for the Universal Law of Gravity is Newtons (N), which represents the force of gravitational attraction between two objects.
How is poisson distribution related to binomial distribution?
The Poisson distribution is a limiting case of the binomial distribution when the number of trials is very large and the probability of success is very small. The Poisson distribution is used to model the number of occurrences of rare events in a fixed interval of time or space, while the binomial distribution is used to model the number of successful outcomes in a fixed number of trials.
What is the power formula for radioactivity?
The power formula for radioactivity is given by P = λ*N, where P is the power, λ is the decay constant, and N is the number of radioactive atoms. This formula represents the rate at which energy is released by radioactive decay.
What does a gradient of 0.5 show on a log log graph?
A gradient of 0.5 on a log-log graph indicates a power-law relationship between the variables being measured. This means that the relationship between the variables is proportional to the square root of one variable raised to the power of 0.5.
Define binomial theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial: that is, the expansion of an expression of the form (x + y)^n where x and y are variables and n is the power to which the binomial is raised. When first encountered, n is a positive integer, but the binomial theorem can be extended to cover values of n which are fractional or negative (or both).
What is n raised to the power n-1?
n-1 = 1/n
A number raised to the ninth power?
n to the power of 9
What is Cardinal number raised to power 30?
It is n^30 where n is the cardinal number.
What is a binomial coefficient?
A binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)^n.
Why is 7 to the power of 0 1?
Why is 7^0 = 1 Algebraic proof. Let 'n' be any value Let 'n be raised to the power of 'a' Hence n^a Now if we divide n^a by n^a we have n^a/n^a and this cancels down to '1' Or we can write n^(a)/n^(a) = n^(a-a) = n^(0) , hence it equals '1' Remember when the lower /denominating index is a negative power ,when raised above the division line.
Validity of binomial expansion for n less than 0?
The binomial expansion is valid for n less than 1.
The power expended with a barbell is raised 2.0m in 2s is?
n nk
What is binomial expansion theorem?
We often come across the algebraic identity (a + b)2 = a2 + 2ab + b2. In expansions of smaller powers of a binomial expressions, it may be easy to actually calculate by working out the actual product. But with higher powers the work becomes very cumbersome.The binomial expansion theorem is a ready made formula to find the expansion of higher powers of a binomial expression.Let ( a + b) be a general binomial expression. The binomial expansion theorem states that if the expression is raised to the power of a positive integer n, then,(a + b)n = nC0an + nC1an-1 b+ nC2an-2 b2+ + nC3an-3 b3+ ………+ nCn-1abn-1+ + nCnbnThe coefficients in each term are called as binomial coefficients and are represented in combination formula. In general the value of the coefficientnCr = n!r!(n-r)!It may be interesting to note that there is a pattern in the binomial expansion, related to the binomial coefficients. The binomial coefficients at the same position from either end are equal. That is,nC0 = nCn nC1 = nCn-1 nC2 = nCn-2 and so on.The advantage of the binomial expansion theorem is any term in between can be figured out without even actually expanding.Since in the binomial expansion the exponent of b is 0 in the first term, the general term, term is defined as the (r+1)th b term and is given by Tr+1 = nCran-rbrThe middle term of a binomial expansion is [(n/2) + 1]th term if n is even. If n is odd, then terewill be two middle terms which are [(n+1)/2]th and [(n+3)/2]th terms.
How do you find the coefficients of the terms in the binomial expansion?
The coefficient of x^r in the binomial expansion of (ax + b)^n isnCr * a^r * b^(n-r)where nCr = n!/[r!*(n-r)!]
1 plus r raised to power n equals?
Binomial Theorem: 1n + nC1*1n-1*r + nC2*1n-2*r2+......+nCn-1*1*rn-1 + rn Or (1+r)n = 1 + n*r + n(n-1)/2! * r2 + n(n-1)(n-2)/3! * r3 + .......... n(n-1)...(n-k)/k! * rk if n < 1 as you cannot calculate the combinations that easily. This gives an accurate approximation provided that abs(x) < 1.
Program to find n raise to the power m?
P = 1 For K = 1 to M . P = P * N Next K PRINT "N raised to the power of M is "; P
