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is there any sequnce which converges to \pi such that each term of it less than pi
I know the sequnce related with the taylor expansion of the arctan \sum_{i=1}^\infty \frac{(-1)^{i+1}}{(2i-1)}
but this sequnce first term is bigger than pi
why I am looking for such a sequnce because I want to find a_{\alpha} , b_{\alpha} such that
\cup (a_{\alpha} , b_{\alpha} ) = (\sqrt{2} , \pi)
for the \sqrt{2} i was thinking about the taylor series for \sqrt{x}
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
I know the sequnce related with the taylor expansion of the arctan \sum_{i=1}^\infty \frac{(-1)^{i+1}}{(2i-1)}
but this sequnce first term is bigger than pi
why I am looking for such a sequnce because I want to find a_{\alpha} , b_{\alpha} such that
\cup (a_{\alpha} , b_{\alpha} ) = (\sqrt{2} , \pi)
for the \sqrt{2} i was thinking about the taylor series for \sqrt{x}
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