I think that the
1+1+1+1 ...= -1/21+1+1+1 ...= -1/2
question, which at present is a merger of an older 1 upvote/1 (not so highly voted) answer Math SE question and a two days ago migrated from from Physics 5 upvotes/highly upvoted answers question, should be reopend as there is IMHO nothing unclear about the OP asking for an (intuitively understandable) proof that $ 1 + 1 + 1 + 1 \cdots = -\frac{1}{2}$.