The best way to guarantee that your movement from one paragraph to the next is logical is to prepare an outline before you begin writing. If each paragraph refers to a section in your outline, your argument should be understandable. Conclusions should summarize the argument of your paper in a way that reinforces the original thesis statement. The conclusion is not the place to introduce new material. Rather, conclusions should refer to points made throughout the body of the text, match the evidence provided throughout the essay, and support the logic of the opening premise of the argument.
Good writing requires good mechanics.
Such usage is called a 'comma splice,' and grammarians absolutely hate comma splices. Even worse are 'fused sentences,' where two independent clauses are simply mashed together without punctuation. Avoid excessive or extravagant generalizations. Do not make 'always', 'never' or 'everything' claims unless you can back it up. Do not use sexist or biased language.