a sequence xn is defined by x1 a x2 b and xn2 12xn1 xn n 12 then prove xn is a cauchy sequence a

Name: a sequence xn is defined by x1 a x2 b and xn2 12xn1 xn n 12 then prove xn is a cauchy sequence and it is convergent 54457
Uploaded: 2023-02-12T05:29:27-08:00
Duration: 5 min 5 s
Channel: Sri K
Description: a sequence xn is defined by x1 a x2 b and xn2 12xn1 xn n 12 then prove xn is a cauchy sequence and it is convergent 54457

Question

Sri K · Accepted Answer

x1 = a, x2 = b, and xn+2 = 1/2(xn+1 + xn)

Question

A sequence Xn is defined by x1 = a, x2 = b, and Xn+2 = 1/2(Xn+1 + Xn) for n = 1, 2, .... Then prove that Xn is a Cauchy sequence and it is convergent.

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