factorials, square roots, and infinite series
a few math questions
in the binomial expansion theroem equation, basically:
where a+b is the exponent to multiply out a (x+y) binormial, and b+1 is the b'th element in that line in pascal's triangle
a! * b!
how is that equation derived?
is there a way to get a square root of a non-square number without a bunch of trial and error?
in an infinite geometric series, the equation for the sum is:
where r is between 1 and -1, and a is the first element. how is this equation derived? i can only get this far:
sum = a + a*r + a*r^2 + a*r^3 ...
= a(1 + r + r^2 + r^3 ...)