state and explain binomial series
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In mathematics, the binomial series is the Maclaurinseries for the function given by , where is an arbitrary complex number. Explicitly, and the binomial seriesis the power series on the right hand side of (1), expressed in terms of the (generalized) binomial coefficients.
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In mathematics, the binomial series is the Maclaurinseries for the function given by , where is an arbitrary complex number. Explicitly, and the binomial seriesis the power series on the right hand side of (1), expressed in terms of the (generalized) binomial coefficients.
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The binomial coefficientsappear as the entries ofPascal's triangle where each entry is the sum of the two above it.
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of abinomial. According to the theorem, it is possible to expand the polynomial (x + y)ninto a sum involving terms of the form a xb yc, where the exponents b and c arenonnegative integers with b + c = n, and thecoefficient a of each term is a specificpositive integer depending on n and b. For example,

The coefficient a in the term of a xb yc is known as the binomial coefficient  or (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also arise in combinatorics, where  gives the number of differentcombinations of b elements that can be chosen from an n-element set.
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of abinomial. According to the theorem, it is possible to expand the polynomial (x + y)ninto a sum involving terms of the form a xb yc, where the exponents b and c arenonnegative integers with b + c = n, and thecoefficient a of each term is a specificpositive integer depending on n and b. For example,

The coefficient a in the term of a xb yc is known as the binomial coefficient  or (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also arise in combinatorics, where  gives the number of differentcombinations of b elements that can be chosen from an n-element set.
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