Revisiting the Convergence of Infinite Series in Calculus 2

GreenPrint
Messages
1,186
Reaction score
0
Sense e^x=Ʃ[k=0,∞] x^k/k!
then
ln(e^x) = ln(Ʃ[k=0,∞] x^k/k!)
x = ln(Ʃ[k=0,∞] x^k/k!)

is this true?
 
Physics news on Phys.org
GreenPrint said:
Sense e^x=Ʃ[k=0,∞] x^k/k!
then
ln(e^x) = ln(Ʃ[k=0,∞] x^k/k!)
x = ln(Ʃ[k=0,∞] x^k/k!)

is this true?
Sure, but how useful it is, I don't know.

I sense that you don't understand the difference between sense and since.
 
Mark44 said:
Sure, but how useful it is, I don't know.

I sense that you don't understand the difference between sense and since.

I'm not sure that it is useful at all and is why I asked lol. Nope my English is god awful.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top