Question

By recognizing the series below as a Taylor series evaluated at a particular value of x, find the sum of the convergent series.

Answer 1

\[\frac{ 1 }{ 2 }-\frac{ \frac{1}{2}^{2} }{ 2 }+\frac{ \frac{1}{3}^{3} }{ 3 }-\frac{ \frac{1}{4}^{4} }{ 4 }+...+\frac{ (-1)^{n}(\frac{1}{2})^{n+1} }{ (n+1) }\]

Answer 2

closest thing to my memory is sin(1/2) which isn't right

Answer 3

where does the 1/3 and 1/4 come from ?

Answer 4

doesn't seem to fit the ...
\[\sum_{n=0}^{\infty} \frac{(-1)^n (\frac{1}{2})^{n+1}}{(n+1)}\]

Answer 5

https://en.wikipedia.org/wiki/Taylor_series#List_of_Maclaurin_series_of_some_common_functions

Answer 6

oh my mistake. 1/2 is supposed to be constant