binomial expansion

[AntonioLao]

The binomial expansion of (a+b) to the nth power is given by the followings: For n=1, a+b. For n=2, a+2ab+b. For n=3, a+3ab+3ab+b. For n=4, a+4ab+6ab+4ab+b. For n=5, a+5ab+10ab+10ab+5ab+b. It can be noted that the values of the coefficient of the second term follow the arithmetic sequence of natural numbers: 1, 2, 3, 4, 5, ¼ .