Why is the taylor series for ln(x+1) so similar to the tailor series sin(x) or cos(x), yet the functions themselves are not at all?

Question

Why is the taylor series for ln(x+1) so similar to the tailor series sin(x) or cos(x), yet the functions themselves are not at all?

In: 0

Answer 1

To be perfectly honest with you, the Taylor series are really not that similar. The coefficients are very different and sin(x)’s expansion only has odd terms (and cosine’s has only even terms) whereas ln(x)’s Taylor series has even and odd terms.