Numerical Series Expansion

A maclaurin series is an expansion of a function, into a summation of different powers of the variable, for example x is the variable in ex. The maclaurin series would give the exact answer to the function if the series was infinite but it is just an approximation.

Examples can be found on the site linked below.

The Poisson distribution is a discrete distribution, with random variable k, related to the number events. The discrete probability function (probability mass function) is given as: f(k; L) where L (lambda) is the mean and square root of lambda is the standard deviation, as given in the link below: http://en.wikipedia.org/wiki/Poisson_distribution

now i MAY be wrong, but ill go ahead:

Million

Billion

Trillion

Quadrillion

Pentillin

Sectillion

(Don't know the one for 7)

Octillion

And that's all I can figure, hope I was help XP

Edit: It goes by the common scientific naming of multiplicity, just like what is described above, but you don't use the prefixes used for geometry like what is described. You instead use the common prefixes used in naming chemical compounds. Here's the list:

Million

Billion

Trillion

Quadrillion

Quintillion

Sextillion

Septillion

Octillion

Nonillion

Decillion

Undecillion

Duodecillion

and so on and so forth...duodecillion is actually 10,000,000,000,000,000,000,000,000,000,000,000,000,000 so if you need to really count anything more than that you're probably at a molecular level and would simply call it 10 to the 39th power.

:)

The gamma function is an extension of the concept of a factorial. For positive integers n, Gamma(n) = (n - 1)!The function is defined for all complex numbers z for which the real part of z is positive, and it is the integral, from 0 to infinity of [x^(z-1) * e^(-x) with respect to x.

means equal the standard deviation

You can find the coefficients of an expanded binomial using the numbers in Pascal's triangle. 1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1 These are a few rows of Pascals triangle. Now let's look at a few binomials, expanded to the second and third powers. (a+b)2=a2 +2(ab) + b2 notice the coefficients are the numbers in the second row of the triangle above. (a+b)3= a3+3(a2b)+3(ab2)+b3 and once again note that the coefficients are the numberin the third line of Pascal's triangle. The first line, by the way, which is 1,1 is the coefficient of (a+b)1 This will work for any power of the binomial. There are generalized form for non-integer powers.

Because "n" is very large and "p" is very small. where "n'' indicates the fixed number of item. And ''p'' indicates the fixed number of probability from trial to trial.

1. Each outcome must be classified as a success (p) or a failure (r),
2. The probability distribution is discrete.
3. Each trial is independent and therefore the probability of success and the probability of failure is the same for each trial.

The Poisson distribution is discrete.

The absolute value of the common ratio is less than 1.

with n=15 as fixed, as p=0.5 changes to p=.05 the binmomial distribution will shift to the right.

It depends on the series.

Use the rule

U2n-1 = (9n2 - 13n + 8)/2

U2n = (9n2 - 13n + 8)/2

The next number is 50.

2203 in base 10, converted to base 5 is 323032203 in base 5, converted to base 10 is 303.

They are variables that can take quantitative - as opposed to qualitative values. For example, the colour of peoples' eyes is a qualitative variable, but their age or shoe size are quantitative variables.

Poisson and Binomial both the distribution are used for defining discrete events.You can tell that Poisson distribution is a subset of Binomial distribution.

Binomial is the most preliminary distribution to encounter probability and statistical problems.

On the other hand when any event occurs with a fixed time interval and having a fixed average rate then it is Poisson distribution.

it is what we now call factor rationalising

A geometric series represents the partial sums of a geometric sequence. The nth term in a geometric series with first term a and common ratio r is:T(n) = a(1 - r^n)/(1 - r)

A skewed bell shape.

Let's say Un=aqn and Sn=a+aq+aq2+aq3+aq4+aq5+...+aqn

Sn = a (1+q+q2+q3+q4+q5+...+qn)

A=(Sn/a) - q (Sn/a) = (1+q+q2+q3+q4+q5+...+qn) - q(1+q+q2+q3+q4+q5+...+qn)

A=1+q+q2+q3+q4+q5+...+qn-q-q2-q3-....-qn-qn+1=1-qn+1

So A = 1-qn+1 = Sn/a (1-q)

So Sn = a (1-qn+1)/(1-q)

The binomial distribution is a discrete probability distribution. The number of possible outcomes depends on the number of possible successes in a given trial. For the Poisson distribution there are Infinitely many.

827/1000 is another way of writing it

There can be no solution to geometric sequences and series: only to specific questions about them.