Differentiating and integrating sums

[ghost]

>>> diff(Sum(x**k, (k,0,oo)).doit(), x)
⎧    1                  
⎪─────────   for │x│ < 1
⎪        2              
⎪(-x + 1)               
⎪                       
⎪  ∞                    
⎪ ____                  
⎨ ╲                     
⎪  ╲      k             
⎪   ╲  k⋅x              
⎪   ╱  ────   otherwise 
⎪  ╱    x               
⎪ ╱                     
⎪ ‾‾‾‾                  
⎩k = 0                  
>>> diff(Sum((-1)**n*sin(n*x)/n, (n,1,oo)).doit(), x)
  ∞                 
 ___                
 ╲                  
  ╲       n         
  ╱   (-1) ⋅cos(n⋅x)
 ╱                  
 ‾‾‾                
n = 1                            
>>> integrate(Sum((-1)**k*x**k, (k,0,oo)).doit(), (x,0,1))
Traceback (most recent call last):

  File "<ipython-input-29-af18c14c7097>", line 1, in <module>
    integrate(Sum((-1)**k*x**k, (k,0,oo)).doit(), (x,0,1))

  File ".\sympy\integrals\integrals.py", line 1295, in integrate
    risch=risch, manual=manual)

  File ".\sympy\integrals\integrals.py", line 486, in doit
    conds=conds)

  File ".\sympy\integrals\integrals.py", line 767, in _eval_integral
    return f._eval_integral(x)

  File ".\sympy\functions\elementary\piecewise.py", line 200, in _eval_integral
    return self.func(*[(integrate(e, x), c) for e, c in self.args])

  File ".\sympy\functions\elementary\piecewise.py", line 200, in <listcomp>
    return self.func(*[(integrate(e, x), c) for e, c in self.args])

  File "C:\Users\Roland\Anaconda3\lib\site-packages\sympy\integrals\integrals.py", line 1295, in integrate
    risch=risch, manual=manual)

  File ".\sympy\integrals\integrals.py", line 486, in doit
    conds=conds)

  File ".\sympy\integrals\integrals.py", line 919, in _eval_integral
    result = manualintegrate(g, x)

  File ".\sympy\integrals\manualintegrate.py", line 1223, in manualintegrate
    return _manualintegrate(integral_steps(f, var))

  File ".\sympy\integrals\manualintegrate.py", line 1013, in integral_steps
    fallback_rule)(integral)

  File ".\sympy\strategies\core.py", line 85, in do_one_rl
    result = rl(expr)

  File ".\sympy\strategies\core.py", line 85, in do_one_rl
    result = rl(expr)

  File ".\sympy\strategies\core.py", line 65, in null_safe_rl
    result = rule(expr)

  File ".\sympy\integrals\manualintegrate.py", line 747, in trig_substitution_rule
    b_positive = ((b.is_number and b > 0) or b.is_positive)

  File ".\sympy\core\expr.py", line 301, in __gt__
    raise TypeError("Invalid NaN comparison")

TypeError: Invalid NaN comparison
>>> integrate(Sum((-1)**k*x**k, (k,0,oo)).doit(), (x,0,1))
Traceback (most recent call last):

  File "<ipython-input-33-af18c14c7097>", line 1, in <module>
    integrate(Sum((-1)**k*x**k, (k,0,oo)).doit(), (x,0,1))

  File ".\sympy\integrals\integrals.py", line 1295, in integrate
    risch=risch, manual=manual)

  File ".\sympy\integrals\integrals.py", line 553, in doit
    evalued = Add(*others)._eval_interval(x, a, b)

  File ".\sympy\functions\elementary\piecewise.py", line 272, in _eval_interval
    int_expr = self._sort_expr_cond(sym, a, b)

  File ".\sympy\functions\elementary\piecewise.py", line 343, in _sort_expr_cond
    lower, upper = cond.lts, cond.gts  # part 1: initialize with givens

AttributeError: 'And' object has no attribute 'lts'
>>> Sum(integrate((-1)**k*x**k, (x,0,1)), (k,0,oo)).doit()
  ∞                
_____              
╲                  
 ╲          1      
  ╲         ⌠      
   ╲      k ⎮  k   
   ╱  (-1) ⋅⎮ x  dx
  ╱         ⌡      
 ╱          0      
╱                  
‾‾‾‾‾              
k = 0