10. Which of the following statements is /are not true?I. Every convergent sequence is Cauchy.II. Every bounded sequence is convergent.III. Every Cauchy sequence is convergent.A. I onlyВ. I onlyC. II and III onlyD. I, II and IIIE. None of the above choices A, B,C or DLet an be a sequence of real numbers such that an+1 2 an, Vn 2 1 and a, + a asn → 0o. Use this preamble to answer questions 11 and 1211. Which of these statements best describe(s) an as a Cauchy sequence?I. for any given e > 0,3 n(ɛ) ER 3|an - a |< e Vn 2 n(e).II. for any given e > 0,| an – Am |< € V m, n > N, for some NERIII. | an – am +0 as m,n +0A I and II onlyB. I and III onlyС. I onlyD. III onlyE. None of the above choices A, B,C or D12. Which of the choices below give(s) the best definition of convergence of a,?I. for any given e > 0,3 n(ɛ) E R Ə|an – a |< e Vn 2 n(e).II. for any given e > 0,3 n(e) E R =|, – am |< e Vn 2 n(e).III. for any give e > 0, 3 n(e) ER 3 a- e< an < a+e Vn 2 n(e).A. I onlyB. I and III onlyС. I onlyD. I, II and IIIE. None of the above choices A, B,C or DLet z1 = 1 and r,n+1 = VIn +2, V n 2 1. Let P, : Tn+1 > In V n e N, be astatement that is either true or false. Use this preamble to answer questions 13,14,15 and 16.13. To prove that P, is true for all n eN, which of the following do you consider as thebase step?A. 12 < #1B. 3 >1C. Ik+1 > Ik-D. Ik+2 > k+1E. None of the above.

Name: 10. Which of the following statements is /are not true?I. Every conve
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Description: 10. Which of the following statements is /are not true?I. Every convergent sequence is Cauchy.II. Every bounded sequence is convergent.III. Every Cauchy sequence is convergent.A. I onlyВ. I onlyC. II and III onlyD. I, II and IIIE. None of the above