Question

Determine whether the following SERIES converge or diverge. Your work should include:

1) the name of the test used

2) the execution of the test and any conditions required for execution

3) the conditions for convergence/divergence

4) conclusion

2 3 6) Please use the integral test for this series; it is not necessary to find the derivative to conclude the function is n(inn) decreasing, but you must state the 3 conditions required. n=2

Answer 1

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because n=2 ndun)? take ten) = 3 on 1200 o teus is continuous on [2,00? ncluu)² 2 few to tuz, 2, niluns ² 40 on [2,00) t (hun) on [2,00 2 & no on [2,00) So, nlnu ²0 on [2,00) So и де) и Lлли) 3 7-6 with on [2,0) on, M. G. 2, 1o, fengs strictly 6. let n, cn₂ 70 on [2,00) Then toget रण ozunien (hin is an increasing (hin, ² < (hun)² SN, E [2,00) function nhing na (hinn) So, unzo bul, 7o. M, (мм, - M, L и. nching So find is monotonically decreasing of We can apply integral test. take winst I dna at ninn) 7 Alle) < tiny nchin) so t = lu2 no 2 M:00 m 3 + 3 at lim in the mato Ima mool mo m2 t² 0 + 3 Una is finite So By integral best given series is convergent