1) A careless student gives the following as a proof of the squeeze theorem. Fin

Question

1) A careless student gives the following as a proof of the squeeze theorem. Find the flaw: "If lim sn - lim tn,then take the limits in the inequality to get L im r L. This can only be true if lim n L 2) Suppose that limo > 0. Show that sn 00 3) Let sn be a sequence of positive numbers. Show that the condition Sn+1 lim 1L 1 implies that Sn 0. and tV1+ tn-1. Does the 4) Define a sequence tn recursively by setting sequence converge? To what? 1-3-5-(2n-1 sequence T converge? Expl 6) Define e = linn(1+-)". Show that 2

Explanation / Answer

tn 2 = 1+ tn-1

when n is infinity tn = tn-1 = c (say )

c = (1+c)0.5 => c2 = 1 + c => c2 - c - 1 = 0

=> (c-0.5)2 = 1+ (0.5)2 = 1.25

=> c = 0.5 + - (1.25)0.5

=> c = - 0.61 (rejected ) cannot be negative , 1.61

Hence the sequences converges to 1.61.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.