The number 180000 (180,000) is spelled "one hundred and eighty thousand".
(The alternate is "one hundred eighty thousand" which may be less clear without hyphenation.)
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+ + nCnbn
The coefficients in each term are called as binomial coefficients and are represented in combination formula. In general the value of the coefficient
nCr = 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-rbr
The 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.
Sounds pretty sexy, eh? See link. http://en.wikipedia.org/wiki/Binomial_expansion
Let's assume that you want the sum of the general harmonic series:
sum(n=0,inf): 1/(an+b)
Since we know that the harmonic series will converge to infinity, we'll also assume that you want the sum from 0 to n.
double genHarmonic(const double n, const double a, const double b) {
double sum = 0.0;
// perform calculations
int k;
for(k = 0; k <= n; ++k) {
sum += 1.0 / (a * k + b);
}
return sum;
}
Harmonic convergence is when the two spirit portals connect from the north and south poles in the spirit world. It is known to have a tree of time which can bring you back to any of the memories in your life. The ancients would meditate under the tree and connect with the great cosmic energy.
its so simple....
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
.........................................
that is pascal's triangle coeffient law......just sum the two numbers and answer is yours
U1 = a = 21
U6 = ar5 = 352947
where Un is the nth term, with first term, a, and commn ratio r.
Dividing the second equation by the first, r5 = 16807
Taking the fifth root, r = 7.
The S6 = a*(r6 - 1)/(r - 1) = 21*(76-1)/(7-1) = 411768
Yes. If the Maclaurin expansion of a function locally converges to the function, then you know the function is smooth. In addition, if the residual of the Maclaurin expansion converges to 0, the function is analytic.
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.
When we do a Fourier transformation of a function we get the primary term which is the fundamental frequency and amplitude of the Fourier series. All the other terms, with higher frequencies and lower amplitudes, are the harmonics.
The moment generating function for any real valued probability distribution is the expected value of e^tX provided that the expectation exists.
For the Type I Pareto distribution with tail index a, this is
a*[-x(m)t)^a*Gamma[-a, -x(m)t)] for t < 0, where x(m) is the scale parameter and represents the least possible positive value of X.