MATH 1020U Chapter Notes - Chapter 11: Conditional Convergence, Ratio Test
Document Summary
Absolute convergence and the ratio and root tests (section 11. 6 of stewart) 1n a is absolutely convergent, then it is convergent. n. 1n a is convergent, but n n. 1 a isn"t, then this is called conditionally n convergent. We are not going to consider this case in this course. ] We are now ready to introduce 2 more tests to determine where a given series is absolutely convergent. The ratio test: if lim n a n. 1n a is absolutely convergent. n: if lim n a n. 1n a is divergent. n a: if lim 1 . , the ratio test is inconclusive: that is, no conclusion can be drawn about the convergence or divergence of . The 2nd test that we introduce works best when each term has an nth power. The root test: if lim n an n. 1n a is absolutely convergent. n: if lim n an n.
