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Math 106 BC Quin'07 pase 1 11/19/2010 Name__5¥450stel sduhons Circle your Section: B (llam) C (noon) la. Does the geometric series 2/3 + 4/9 + 8/27 + --- converge? If so, to what? I nas es : 5 eS z Serts LHS 4 goomene Snes wile a-% Mor A} che | | | sa ta 5 4-D yet A i Bs Be Ame? pot ~ TR A oT oo ke 1b. Explain whether the comparison test tells us that the series eRe nk compared to the series in (la). (Verify any inequalities you claim hold for the individual terms) gn a tern by- str ba, feat. 2 3, bor each K, pe bale, 28 2 2° Auk Shee oR am eae Ja converges, diverges, or is of no help, when 3k 3% , Ke! va a ike and ewe lim yk amvige Ak : ah3" § 2h 3K hk <> Y 2 sek term by team, aa $ a yet Concho 2 shu © 29%, 0 § 26 MK ehh is tne, Shee Kv,| balk 2% 8 hK we xO 0 2a. Consider the series }> a, = V4/4 + V5/5 + V6/6 + V7/7 + V8/8 + ---. Use the integral test and an appropriate 4 function f(z) for which a, = f(k) to decide if the series diverges. ts ; B nsiders f ee Pde odin (Fk lin ax*] ~ 4 Bae ly x* ~ Ba” f Rae 4 VE = fiw 2 VB - Y= & {2 Ax clvegea ; te inteyeol fate Sigs ae « atte 2b. If the series in 2a diverges, use the method i a glass which uses the corresponding integrals to find a B for which Deo ak is bigger than 20. Brey « VK te HAMOOT fr N/3/2.010, which we Knew Ls X dK 28 aes oo Si aap bt B ath lia Io < ie 2B a 12 
