Question
Part 1: Part 2: Using the alternating series test, test the convergence of D1 () Show...
Part 1:
Part 2:
Using the alternating series test, test the convergence of D1 () Show all your work
Using the definition of convergence of a series, test the convergence of If it converges, find its value. 1 1 100 no 1+2 1+3
Answers
9) Į EUR Ź + Egon n=2 alternating Serres. n²4 n3ry 20 E 6159 an. wt na2 e finite value. u thus converges then Eton an also converges. it n=2 an n34 Condition ① an to for all ny2 an-ant 234 1 の+1アーム n²4 (1431+30- n3 +35² +32-3-nity (134) (n?+Bn43n-3) 30²+3ntl an- anti zo. for all in. (134)[%+353 +3n-3) an-ant to for all n. an> anul Te Condition Azt may as an is a monotone decreasing funchon As conclition ♡ €@ are valid, we can apply alternating Scores test. lim an tim h00 FO, n²4 ntona2 SEDan Converges herce Ž Goh ni nzy 2). also converges. Ang co ENT ㅗ ht2 S an. n+2 n=1 an n+2 n3 6+3) - (142) (h+2)(n+3) 70. for all ny (+2)(n+3) anto. an-anel nitz nis) -( how) n13 htu = 2 t. ㅗ n+2 (n+3) nty (n° +70+12) -2(146n+8) + (n?+ 5576) (+2) (213) (+4) = 2 (n+2) (273) (nt") > for all n. an-amal ro. for all n. an> anii an 9,7 ay az decreasing Sequence if its lower bound is zero then series is convergent a monotoniclim lim an a ny ( mitte mi) hence, the series is Convergent. Ang a, 3 Cancels ouf a Az Š - Ś an 11 n72 NAB n Sn = E an ģ- I n13 n= tim Sn= So = u IMO Zan= lim (3 - 773) 100 -اجرا hata ning n+2 12 n=1 3 Ang the series Converges to Wh
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