Repository: sympy/sympy

Issue:
Sum(1/log(log(n)), (n, 22, oo)).is_convergent() not implemented
`>>> Sum(1/log(log(n)), (n, 22, oo)).is_convergent()`
Traceback (most recent call last):

  File "<ipython-input-19-50f193f491f8>", line 1, in <module>
    Sum(1/log(log(n)), (n, 22, oo)).is_convergent()

  File ".\sympy\concrete\summations.py", line 528, in is_convergent
    "is not yet implemented" % (sequence_term))

NotImplementedError: The algorithm to find the Sum convergence of 1/log(log(n)) is not yet implemented



Could someone please tell me the way to put the whole thing in code form
When I try to put the whole thing in code form, with that symbol under the tilde at the start and at the end , then none of it appears in code form

Is this a flaw in the is_convergent program
That whenever it encounters a sum whose convergence is unknown, it cause an error 

Discussion:

Patch:
diff --git a/sympy/concrete/summations.py b/sympy/concrete/summations.py
index 79e1e51ff4..8ce0cc33d1 100644
--- a/sympy/concrete/summations.py
+++ b/sympy/concrete/summations.py
@@ -439,10 +439,11 @@ def is_convergent(self):
         next_sequence_term = sequence_term.xreplace({sym: sym + 1})
         ratio = combsimp(powsimp(next_sequence_term/sequence_term))
         lim_ratio = limit(ratio, sym, upper_limit)
-        if abs(lim_ratio) > 1:
-            return S.false
-        if abs(lim_ratio) < 1:
-            return S.true
+        if lim_ratio.is_number:
+            if abs(lim_ratio) > 1:
+                return S.false
+            if abs(lim_ratio) < 1:
+                return S.true
 
         ### --------- p-series test (1/n**p) ---------- ###
         p1_series_test = order.expr.match(sym**p)
@@ -459,6 +460,15 @@ def is_convergent(self):
             if p2_series_test[p] <= 1:
                 return S.false
 
+        ### ------------- Limit comparison test -----------###
+        # (1/n) comparison
+        try:
+            lim_comp = limit(sym*sequence_term, sym, S.Infinity)
+            if lim_comp.is_number and lim_comp > 0:
+                    return S.false
+        except NotImplementedError:
+            pass
+
         ### ----------- root test ---------------- ###
         lim = Limit(abs(sequence_term)**(1/sym), sym, S.Infinity)
         lim_evaluated = lim.doit()


Test patch:
diff --git a/sympy/concrete/tests/test_sums_products.py b/sympy/concrete/tests/test_sums_products.py
index b0da5c2e22..fc784faf0f 100644
--- a/sympy/concrete/tests/test_sums_products.py
+++ b/sympy/concrete/tests/test_sums_products.py
@@ -1016,3 +1016,9 @@ def test_issue_14112():
     assert Sum((-1)**n/sqrt(n), (n, 1, oo)).is_absolutely_convergent() is S.false
     assert Sum((-1)**(2*n)/n, (n, 1, oo)).is_convergent() is S.false
     assert Sum((-2)**n + (-3)**n, (n, 1, oo)).is_convergent() is S.false
+
+def test_issue_14111():
+    assert Sum(1/log(log(n)), (n, 22, oo)).is_convergent() is S.false
+
+def test_issue_14484():
+    raises(NotImplementedError, lambda: Sum(sin(n)/log(log(n)), (n, 22, oo)).is_convergent())