Sum doit for series which are demonstrably divergent

[ghost]

>>> Sum(((-1)**k), (k, 0, oo)).is_convergent()
False
>>> Sum(((-1)**k), (k, 0, oo)).doit()
  ∞        
 ___       
 ╲         
  ╲       k
  ╱   (-1) 
 ╱         
 ‾‾‾       
k = 0      

Returning the given expression gives no information to the user
If the convergence check was run after the summation failed, then useful information would have been provided to the user