Question

7. Determine whether the following series converge or diverge. Show your work for full credit. State the test you use and show the reasoning that allows you to use that test. a) o ni+sin(n) a 2n=1 4+2n-1 Joo 52n+3 c) c) n=1 (2n)!

Answer 1

n²+ sin(n) 74+2n-1 apply Series Comparison test san, Ebn positive, an <bn 2 if Ebn conlenge, so does san .. San diverge, so does Ebn niti -1 < Sin(n) = 1 → eu n't sin (n) < Ž. na n4+2n- n=1 nt+2n-1 apply Series Comparison test X n=1 no noz (cha1) emai) Encan)

- 2016-17 2Cht) Expand telesmping Sowes : given Series Converges i by Series Comparison test , given 8 m+sin(n) is. Conierges 74+27-1 Series z Ž 52013 n=1 ... (2n)! apply Series statio test. naN, an to, hanno b .: if Lel, then sain conlenges b>1.; tan diverges. . (n+D + 31 (2(n+1))! 52043 ani a(n+1)(2n+i)! 25 se lacas coms) - 0 in hoc1. so by the oratio test given series n=1 Thank you