I am trying to calculate the 11th derivative, , of a function using the Taylor Series centred at one.
I arrived to this stage where I form it into a geometry series format:
From here, I believe that the is essentially the r in a geometry series formula.
So I put that into a summation:
I cleaned it up a little bit and manipulated the algebra and arrived at:
Now, this looks like a Taylor Series format to me with at the back and as my co-efficient.
Since I got the co-efficient of the series, I thought I could just do this:
and then get:
However, my answer is wrong and when I do it on a calculator,
What should I do after this? I thought I can get the answer once I turn it into a format that looks like the original Taylor series format and find the answer from the co-efficient?