Is the convergence rate of a series and its alternating counterpart same.
For example is the convergence rate of \zeta(2) and \eta(2) both equal.

What about the case \zeta(1) and \eta(1) where one is divergent and the latter is convergent to \ln(2)

Will the rates of convergence be equal to both \zeta(s) and \eta(s) for s\geqslant 2

Thanks