Learn why we cannot draw any conclusion if L=0 or L=infinity when we use the limit comparison test. Remember, for the limit comparison, we check the limit of an/bn. And if the limit is finite and greater than 0, then we can say either the series of an and series of bn both converge or both diverge. But check out the series of sin^2(1/n). If we compare this with the series of 1/n, then we will get L=0 (or L=infinity if we compute limit bn/an instead). If we want to say that the series of sin^2(1/n) and series of 1/n both converge, then we will be drawing the wrong conclusion.
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