Explain binomial series.

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The Binomial Theorem is the method of expanding an expression which has been raised to any finite power. A binomial Theorem is a powerful tool of expansion, which has application in Algebra, probability, etc.
Binomial expansion
The Binomial Expansion Theorem is an algebra formula that describes the algebraic expansion of powers of a binomial. According to the binomial expansion theorem, it is possible to expand any power of x + y into a sum of the terms. The Binomial Expansion Formula or Binomial Theorem is given as:
$[(x + y)^{n} = x^{n} + n x^{n - 1} y + f r a c n (n - 1) 2! x^{n - 2} y^{2} + \dots + y^{n}]$

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1 + \frac{1}{3} + \frac{1}{3} \cdot \frac{3}{6} + \frac{1}{3} \cdot \frac{3}{6} \cdot \frac{5}{9} + . . .

C_{0}, C_{1}, C_{2} . . .

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\frac{2 C_{0}}{1} + \frac{3 C_{1}}{2} + \frac{4 C_{2}}{3} + \frac{5 C_{3}}{4} + . . . +

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