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?

thanks!