Set up expansion formula for Taylor Series #f(x)=\root(3)(x)# centered round #a=1#?
So far I have the exponent as #x^(-2/3-n)# , and the denominator as #3# . But the rest in the numerator?
What kind of factorial is #(1*2*5*8*....)# ?
So far I have the exponent as
What kind of factorial is
1 Answer
Explanation:
We see that the derivatives alternate signs after the first term and the
Furthermore, the exponent can be represented by
The denominator involves
For the numerator, a distinct pattern emerges if we disregard
It can't be represented by a factorial (or even double factorial), but we can use the following notation to indicate the terms all have differences of
We have
So,
Thus, using the standard form of a Taylor Series about
However, if we take the above summation at