asymptotic expansion

A series of the form c₀ + (c₁/x) + (c₂/x²) + . . . + (c_n/xⁿ) + . . . often used for formal solution of differential equations or for function approximation when is large.
Though such series are divergent, terms initially decrease in size to one of minimum value at which term the series can be truncated to obtain a useful approximation.