Power Series

[Jason76]

When differentiating the factorials on the bottom are reduced by 1. For instance, \(\displaystyle 5!\) becomes \(\displaystyle 4!\). Why is this so?



What kind of addition is going on the bottom line to produce it's result?

 

[stapel]

View attachment 3592

When differentiating the factorials on the bottom are reduced by 1. For instance, \(\displaystyle 5!\) becomes \(\displaystyle 4!\). Why is this so?

What did you get when you differentiated (x^3)/(3!)? Then (x^5)/(5!)? And so forth. What were your results of your efforts?

View attachment 3594

What kind of addition is going on the bottom line to produce it's result?

The bottom line says "0.5 - 0.0069 is approximately equal to 0.493". What is your quarrel with this?

 

[Quaid]

\(\displaystyle 5!\) becomes \(\displaystyle 4!\). Why is this so?

Cancellation of factors. Please show your differentiation of that term.

Cheers :cool: