Series rapresentation $f(t)=\frac{1}{(2t+1)^{2}}$ How to find the series rapresentation in $t=0$ of the following expression
$$f(t)=\frac{1}{(2t+1)^{2}}$$
Can someone show me also the steps.
Thank you so much!

Writing f(t) as power instead of as quotient it is easier to calculate the successive derivatives:
$$f(t) = (2t+1)^{-2}$$
$$f'(t) = (-2)(2t+1)^{-3}2$$
$$f''(t) = (-3)(-2)(2t+1)^{-3}2^2$$
$$f^{3}(t) = (-4)(-3)(-2)(2t+1)^{-3}2^3$$
$$\cdots$$
$$f^{n}(t) = \cdots$$
Can you continue?
