#2part b Math4303Sec4_1Homework Protected View - Saved to this PC -O SearchgnLayoutReferencesMailingsReviewViewHelpe Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View.Enable EditingMath 4303 Homework Section 4.1 Convergence1. Write out the first seven terms of the sequence dn2n +1%3D3n-12. Using only Definition 4.1.2 (N-ɛ definition of convergence), prove the following:ka] lim- = 0kER4n +1b] limno n+3= 46n? +3n= 3no 2n? -5c] limsin( n)=D0d] lim3. Prove or provide a counterexample for the following:a] If (s,) converges then (s) converges.b] If (s,) converges then (s,) converges.c] lim s, = 0 iff lim |s„ =04. Suppose that lim s, =0 and suppose that (t, ) is a bounded sequence. Show that lim s,t, = 05. Suppose that (x,), (y, ), and (=,) are sequences such that x, Sy, S=, n and lim x, = L = lim =Show that lim y, = L6. Suppose that lim s. =s where s > 0. Prove that there exists a natural number N, such thatif n> N, then s, > 0DFocusDELL

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Description: #2part b Math4303Sec4_1Homework Protected View - Saved to this PC -O SearchgnLayoutReferencesMailingsReviewViewHelpe Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View.Enable EditingMath 4303 Homework Section