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Lord, 1985, 213—214, and also A. E. Parks, 1986, 722—723. EXERCISES 4 1. Let and be convergent series. Show that (a) (b) ME converges if, and only if, 2. Show that converges for every NEI%J. 3. Can "nonnegativity" be dropped in Proposition 6? In Corollary 7? 4. Use Example 3 and Corollary 7 to show that diverges. 5. Check the following series for convergence or divergence: (a) (c) - k1 iOOk+i ( k=1 " + 1) (b) k=l +1— k1 00 (e) i)(2k + 1) (d) k=l 00 )/k2 i/(2k + 1) (f) k=1 Introduction to Real Analysis 48 6.

There is N1 such that k N implies Il/Yk-1/YI = IYkYI/IYYkI 1yky1/IYIB

K }. Show } that converges to 2. 2. /kk, does {xk+1/xk } converge? If so, what is its limit? 23. If Xk x and x

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