Binomial Theorem

Pascal's Triangle is not a geometrical

Pascal's Triangle is not a geometrical triangle but a triangle of numbers arranged in a definite pattern. The row numbers start from 0, and the number

The coefficients in the binomial theorem

The coefficients in the binomial theorem are written as nCr, where nCr = n! / [r!(n-r)!]. The value at the nth row and (r+1)th place of Pascal's Trian

For every positive integer n

For every positive integer n, (x+y)^n = nC0 x^n y^0 + nC1 x^(n-1) y^1 + ... + nCn x^0 y^n = sum_{r=0}^{n} nCr x^(n-r) y^r.

The (r+1)th term of the expansion

The (r+1)th term of the expansion of (x+y)^n is T_(r+1) = nCr x^(n-r) y^r.

The rth term from the end

The rth term from the end of the expansion of (x+y)^n is the (n-r+2)th term from the beginning, i.e., T_(n-r+2).