Binomial Theorem is born!!

We have the plague to thank for the binomial theorem! In 1665, plague was raging in England, and Isaac Newton, a new (and undistinguished) graduate of the University of Cambridge, was forced to spend most of the next two years in the relative safety of his family's country manor in Woolsthorpe. It turned out that solitude and free time was just the stimulous Newton's creative brain needed. In that 18-month period of retreat, he came up with his proof and extension of the binomial theorem, invented calculus (which he called his "method of fluxions"), discovered the law of universal gravitation, and proved that white light is composed of all colors. All of this before the age of 25!
Newton was not the first to describe a formula for binomial expansions, or multiplying out any expression of the form (a + b)n. We know, for example, that an Islamic mathematician named al-Karaji (d. 1029) constructed a table of binomial coefficients up to (a+b)5 (that is, Pascal's triangle), and later Muslim mathematicians credited him with discovering the formula for the expansion of (a + b)n. Furthermore, in a now lost work, Omar Khayyam (1048-1131) apparently gave a method for finding nth roots based on the binomial expansion and binomial coefficients. Ancient Indian and Chinese mathematicians also knew the binomial theorem. And in Europe, already a century before Newton's birth, Blaise Pascal's Treatise on the Arithmetical Triangle provided a handy way to generate binomial coefficients. All of these methods for binomial expansion, however, work only for positive integer values of n. What Newton discovered was a formula for (a+b)n that would work for all values of n, including fractions and negatives: (a+b)n = an + nan-1b + [n(n-1)an-2b2] / 2! + [n(n-1)(n-2)an-3b3] / 3! + . . . + bn For -1.