Question

What is the difference b/w "Binomial Series" and "Binomial Theorem"? Also give formula for each.

Answer 1

Step-by-step explanation:

$\huge{\underbrace{\overbrace{\mathfrak{\pink{Answer:}}}}}$

The binomial theorem states that for some a,b∈R and some k ∈Z+ ,

(a+b)k=∑n=0k(kn)ak−nbn.

The binomial series allows us to use the binomial theorem for instances when k is not a positive integer. The binomial series applies to a given function f(x)=(1+x)k for any k∈R with the condition that |x|<1 . It is stated as follows:

(1+x)k=∑n=0∞(kn)xn .

Note that the binomial theorem produces a finite sum and the binomial series produces an infinite sum.