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math formula sheet

math formula sheet - Chapter 10 M.W S.R B.S lntegral...

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Chapter 10 M.W., S.R., B.S. lntegral Test:for functionsthal are nonnegatiu" *Ja*tl \rf Ii fx)dx converges, rn"np,o* converges ryn[i1ryt diverges, then-f ,a. diverges L omparison resl: for),b* and ),a, series ofpositive tenns 00 l) If) , 6, converges and a, s b, for every positive integer k, th"n f, o* "onn"rg", 9a ll) If I I br diverges and ar2 b, for every positive integer t. tt en B a, diverges Ltmit ( ontpa rison lesl: I,6, and X,a* series of positive rerms & thar lim f =l I) Ifl is a positi'e constant. then series are either both convergent or divergenr :c Il) If a = 0 andl, b^ converges, th"nf,o, converges t-tp*:* . undT, 6, diu".Bes, then!, a, diverees Rotiokst: for! a* is a series ofpositive terms such th;t ilE L-r " - *7-L n q)q, I) lfZ< I , the series is convergent ll) If L >1. or if lim 1, ' =6lheseries isdivergent ,t 4t un lll) ll-1.=1. thercsr is inconclusive Root Test'. at F=,o, is a series of positive rerms such thattim (p- I) IfI< l. rhe series is convcrgent It) lfZ: I . rhe tesl is inconclirsivE , lf L> | . or rf Iim ,iJ{, = cO . rhe series is divergenr
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nth Term kst a lf lim a., ./ 0. then ,) , a. diveryes
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