{"action":"created","comment":{"url":"https://api.github.com/repos/sympy/sympy/pulls/comments/168344892","pull_request_review_id":96696742,"id":168344892,"diff_hunk":"@@ -401,6 +403,10 @@ def is_convergent(self):\n             lower_limit = -upper_limit\n             upper_limit = S.Infinity\n \n+        sym_ = Dummy(sym.name, integer=True, positive=True)\n+        sequence_term = sequence_term.xreplace({sym: sym_})\n+        sym = sym_\n+","path":"sympy/concrete/summations.py","position":16,"original_position":16,"commit_id":"666bf92e93ec5e378baf09e688b1d7430affe5b5","original_commit_id":"666bf92e93ec5e378baf09e688b1d7430affe5b5","user":{"login":"normalhuman","id":13082030,"avatar_url":"https://avatars1.githubusercontent.com/u/13082030?v=4","gravatar_id":"","url":"https://api.github.com/users/normalhuman","html_url":"https://github.com/normalhuman","followers_url":"https://api.github.com/users/normalhuman/followers","following_url":"https://api.github.com/users/normalhuman/following{/other_user}","gists_url":"https://api.github.com/users/normalhuman/gists{/gist_id}","starred_url":"https://api.github.com/users/normalhuman/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/normalhuman/subscriptions","organizations_url":"https://api.github.com/users/normalhuman/orgs","repos_url":"https://api.github.com/users/normalhuman/repos","events_url":"https://api.github.com/users/normalhuman/events{/privacy}","received_events_url":"https://api.github.com/users/normalhuman/received_events","type":"User","site_admin":false},"body":"Actually, I think this change would not be needed if the tests used `limit_seq` instead of `limit`, because `limit_seq` already carries out this substitution of an integer dummy. Try replacing `limit` with `limit_seq` in this method, it will probably improve the results without need for dummy replacement.","created_at":"2018-02-14T23:32:57Z","updated_at":"2018-02-14T23:32:57Z","html_url":"https://github.com/sympy/sympy/pull/14158#discussion_r168344892","pull_request_url":"https://api.github.com/repos/sympy/sympy/pulls/14158","author_association":"MEMBER","_links":{"self":{"href":"https://api.github.com/repos/sympy/sympy/pulls/comments/168344892"},"html":{"href":"https://github.com/sympy/sympy/pull/14158#discussion_r168344892"},"pull_request":{"href":"https://api.github.com/repos/sympy/sympy/pulls/14158"}},"in_reply_to_id":167970908},"pull_request":{"url":"https://api.github.com/repos/sympy/sympy/pulls/14158","id":168448446,"html_url":"https://github.com/sympy/sympy/pull/14158","diff_url":"https://github.com/sympy/sympy/pull/14158.diff","patch_url":"https://github.com/sympy/sympy/pull/14158.patch","issue_url":"https://api.github.com/repos/sympy/sympy/issues/14158","number":14158,"state":"open","locked":false,"title":"Implemented Sum((-1)**n/sqrt(n), (n, 1, oo)).is_absolutely_convergent()","user":{"login":"ArighnaIITG","id":28482640,"avatar_url":"https://avatars1.githubusercontent.com/u/28482640?v=4","gravatar_id":"","url":"https://api.github.com/users/ArighnaIITG","html_url":"https://github.com/ArighnaIITG","followers_url":"https://api.github.com/users/ArighnaIITG/followers","following_url":"https://api.github.com/users/ArighnaIITG/following{/other_user}","gists_url":"https://api.github.com/users/ArighnaIITG/gists{/gist_id}","starred_url":"https://api.github.com/users/ArighnaIITG/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ArighnaIITG/subscriptions","organizations_url":"https://api.github.com/users/ArighnaIITG/orgs","repos_url":"https://api.github.com/users/ArighnaIITG/repos","events_url":"https://api.github.com/users/ArighnaIITG/events{/privacy}","received_events_url":"https://api.github.com/users/ArighnaIITG/received_events","type":"User","site_admin":false},"body":"Fixes #14112 .\r\n\r\nThis PR also introduces a new convergence test -- the **Ratio Test**. Actually, when I followed normalhuman's comment on the issue, I solved the particular issue, but I had another problem -\r\n\r\n```\r\n>>> from sympy import *\r\n>>> n = symbols('n')\r\n>>> a = Sum(factorial(n)/5**n, (n, 1, oo))\r\n>>> a.is_convergent()\r\nNotImplementedError : The algorithm to find the Sum convergence of 5**(-_n)*factorial(_n))**(1/_n) is not yet implemented.\r\n```\r\nWhile looking through the file, I then came to realize that the algorithm of **Ratio Test** hadn't been implemented, which can solve this problem easily. So, the code snippet of the Ratio_test algorithm has been implemented, and the issue fixed.\r\n\r\nTest case has also been 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