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**Unformatted text preview: **Chapter 11.1 homework: Sequences The usual even/odd policy applies. #2 #6 {2*4*6*...*(2n)} #8 a_1=4, a_(n+1) = a_n / (a_n-1) #10 {1, 1/3, 1/9, 1/27} #14 {5,1,5,1,5,1,...} #16 {cos(n pi/3)} #20 a_n = n^3 / (n+1) #22 a_n = 3^(n+2) / 5^n #28 a_n = cos(2/n) #29 {(2n-1)! / (2n+1)!} #46 a_n = (-3)^n / n! #52 a_n = 1*3*5*...*(2n-1) / n! #55 annually compounded interest #57 {n r^n}: which values of r make it converge? #59 {a_n} is decreasing and all terms between 5 and 8. #62 a_n = (2n-3) / (3n+4) #64 a_n = n * exp(-n) #66 a_n = n + 1/n #72 just part (b): iterating f(x)=cos(x) hint: your answer should be around 0.739; feel free to use Excel. #80 just part (b): continued fractions (optional) again, feel free to use Excel. Question A Put these sequences in order as to which grows the slowest, second-slowest, etc. ln(n) n^n b^n (with b>1) n! n^p (with p>0) For example, you might say that n^p is the slowest, then ln(n), then n!, then n^n, then b^n "because exponentials always win". But I hope you don't,...

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