## The coefficients in the expansions of (x+y)^n

The ancient Indian mathematicians knew about the coefficients in the expansions of (x+y)^n,<=n<=7.The arrangement of these coefficients was in the form of a diagram called Meru-Prastara, provided by Pingla. The term binomial coefficient was first introduced by the German mathematician, Michael Stipel (1486-1567 A.D.) in approximately 1544 A.D. Bombelli (1572 A.D.) also gave the coefficients in the expansion of (a+b)^n, for n=1,2,....,7 and Oughtred (1631 A.D. ) gave them for n=1,2,3......10. The arithmetic triangle, popularly known as Pascal's triangle.

## we can find a coefficient with pascal triangle

11^0=1

11^1=11

11^2=121

11^3=1331

11^4=14641

11^5=15101051

11^6=1615201561

.......

Binomials

(x + y)

^{n}= a_{0}x^{n}+ a_{1}x^{n}^{−}^{1}y + a_{2}x^{n}^{−}^{2}y^{2}+ .....
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