What is the difference b/w "Binomial Series" and "Binomial Theorem"? Also give formula for each.
1 answer:
Step-by-step explanation:
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.
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Answer:
Step-by-step explanation:
This is where knowing the exponent rules come into play. The negative exponent applies for both 6 and 2.
The negative exponent rule is basically reciprocal of x. So, if x is the numerator, it gets moved to the denominator, and vise versa. Also, the power of a power applies here too with the implied 1st power.