What is series expansion method?

In mathematics, a series expansion is an expansion of a function into a series, or infinite sum. It is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division).

What are expansions in math?

Expansion is an affine transformation (sometimes called an enlargement or dilation) in which the scale is increased. It is the opposite of a geometric contraction, and is also sometimes called an enlargement. A central dilation corresponds to an expansion plus a translation.

What is series expansion Mathematica?

Series can expand about the point x=∞. The result of Series is usually a SeriesData object, which you can manipulate with other functions. Normal[series] truncates a power series and converts it to a normal expression. SeriesCoefficient[series,n] finds the coefficient of the n. -order term.

What is expansion formula?

The binomial expansion formula involves binomial coefficients which are of the form (nk) (or) nCk n C k and it is calculated using the formula, (nk) =n! / [(n – k)! k!]. The binomial expansion formula is also known as the binomial theorem.

What is the series expansion of sin Alpha?

Let us recall the formula of sin (α + β) = sin α cos β + cos α sin β and cos (α + β) = cos α cos β – sin α sin β. Therefore, the expansion of sin (A + B + C) = cos A cos B cos C (tan A + tan B + tan C – tan A tan B tan C).

What is the expansion of Secx?

Answer: sec(x) = 1 + x²/2 + 5x⁴/24 + ………

What is the A in Taylor series?

The ” a ” is the number where the series is “centered”. There are usually infinitely many different choices that can be made for a , though the most common one is a=0 .

Which is an expansion of a Taylor series?

A Taylor Series is an expansion of some function into an infinite sum of terms, where each term has a larger exponent like x, x 2, x 3, etc. ex = 1 + x + x2 2! + x3 3! + x4 4! + x5 5! + (Note: ! is the Factorial Function .)

How are infinite sequences and series expansions different?

Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely. A series expansion is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division).

How to calculate the sum of log expansions?

Summation Expansion Comments x n n = x + (1/2)x 2 + (1/3)x 3 + (1/4)x x n n = – ln (x + 1) (-1 < x <= 1) (-1) n x n n = – x + (1/2)x 2 – (1/3)x 3 (-1) n x n n = – ln (x) (-1 < x <= 1) x 2n-1 2n-1 = x + (1/3)x 3 + (1/ 5)x 5 + x 2n-1 2n-1 = ln ( (1+x)/ (1-x) ) 2 (-1 < x < 1)

How are series used in the study of mathematics?

The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions.