4. (5 marks). Suppose that an and Eb, are series with positive terms. In the Limit...

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4. (5 marks). Suppose that an and Eb, are series with positive terms. In the Limit Comparison Test, if lim = c where c is a finite number and c > 0, n00 then either both series converge or both series diverge. In this question, we'll see that if c = 0, then no specific conclusion can be drawn about the convergence of the two series. For example, Question 48 in Section 11.4 covers the case 'if c = 0 and bn is conver- gent, then an must be convergent', but there are many situations that could occur if c = 0. Give examples of pairs of series E an and Ebn (each with positive terms) where an lim 0, b, n00 so that (a) both an and bn converge; (b) both an and Ebn diverge; (c) Ebn diverges but am converges; 4. (5 marks). Suppose that an and Eb, are series with positive terms. In the Limit Comparison Test, if lim = c where c is a finite number and c > 0, n00 then either both series converge or both series diverge. In this question, we'll see that if c = 0, then no specific conclusion can be drawn about the convergence of the two series. For example, Question 48 in Section 11.4 covers the case 'if c = 0 and bn is conver- gent, then an must be convergent', but there are many situations that could occur if c = 0. Give examples of pairs of series E an and Ebn (each with positive terms) where an lim 0, b, n00 so that (a) both an and bn converge; (b) both an and Ebn diverge; (c) Ebn diverges but am converges;