Consider the series $a_n=(c_1+c_2n^2)^{-1.5}$ where $n\in\mathbb{N}$.
I want to sum the series up to infinity.
$$(c_1+c_2)^{-1.5}+(c_1+4c_2)^{-1.5}+(c_1+9c_2)^{-1.5}+\cdots$$
I really have no idea because the series is neither in the form of $(n-1)d+a_0$ nor is it like $a_0q^{n-1}$.
How can I get the sum value?