- Thread starter
- #1

I know the sequnce related with the taylor expansion of the arctan [tex]\sum_{i=1}^\infty \frac{(-1)^{i+1}}{(2i-1)} [/tex]

but this sequnce first term is bigger than pi

why I am looking for such a sequnce because I want to find [tex]a_{\alpha} , b_{\alpha} [/tex] such that

[tex] \cup (a_{\alpha} , b_{\alpha} ) = (\sqrt{2} , \pi) [/tex]

for the [tex]\sqrt{2} [/tex] i was thinking about the taylor series for [tex]\sqrt{x} [/tex]

but what I am stuck at is the taylor series for a function T(x) is convereges to f(a) if the expansion was around the a

Any ideas

Thanks