ON SMARANDACHE GENERAL CONTINUED FRACTIONS

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ON SMARANDACHE GENERAL CONTINUED FRACTIONS

MaohuaLe Department of Mathematics, Zhanjiang Normal College Zhanjiang, Guangdong, P.RChina.

Abstract. Let A={ an} n=1 and B={b n} n=1 be two Smarandache type sequences. In this paper we prove that if a n+l ~ b n> 0 and b n+l ~ b n for any positive integer n, the continued fraction

a 1 +---a2+ a3 +

(2)

00

is convergent. 00

Let A={ an} n=1 and B={b n} n=1 be two Smarandache type sequences. Then the continued fraction

b1 a 1 + --------------------b2 a 2 + -------------b3 a 3 + --------

(1)

is called a Smarandache general continued fraction associated with A and B (see [1]). By using Roger's symbol, the continued fraction (1) can be written as b1

(2)

b2

a 1 +---a 2 + a 3 + ....

Recently, Castillo [1] posed the following question: 1

Question. Is the continued fractions 1 + ----12 convergent?

176

21

+ 123

321

+ 1234 + ...


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