WebDec 6, 2024 · We obtain the infinite products of the reciprocal of the k - Fibonacci sequence q_ {n} and k - Lucas sequence p_ {n}, when a=b=k. Then, the sequences \Biggl\ { \Biggl ( 1-\prod_ {k=n}^ {\infty } \biggl ( 1-\frac {1} {q_ {k} } \biggr) \Biggr)^ {-1} \Biggr\} _ {n} \quad \textit {and} \quad \ { q_ {n}-q_ {n-1} \} _ {n} (6) Web{cf. Theorem 4) those rational numbers which can be written as finite sums of reciprocals of distinct nth. powers of integers, where n is an arbitrary (fixed) positive integer and "finite sum" denotes a sum with a finite number of summands. It will follow, for example, that p\q is the finite sum of reciprocals of distinct squares1 if and only if
The infinite sum of reciprocal Pell numbers - ScienceDirect
WebMar 15, 2013 · Wenpeng and Tingting [6] gave analogue of the result (1) for the Pell numbers: ∑ k = n ∞ 1 P k - 1 = P n - 1 + P n - 2 if n is even and n ⩾ 2; P n - 1 + P n - 2 - 1 if n is odd and n ⩾ 1. Also the same authors [7] gave the similar results for partial infinite sums including reciprocal squared-Pell numbers. WebSep 2, 2016 · In this paper, we consider innite sums derived from the reciprocals of the … bank raya internet banking
ON THE RECIPROCAL SUMS OF PRODUCTS OF LUCAS NUMBERS …
WebReciprocal sums. Infinite sums over reciprocal Fibonacci numbers can sometimes be evaluated in terms of theta functions. For example, the sum of every odd-indexed reciprocal Fibonacci number can be written as ... Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2. WebOct 23, 2024 · Template:Short description Template:Redirect-distinguish Template:Thumb. In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another … WebJun 26, 2013 · Recently, the authors and studied the infinite sums derived from the Pell … bank raya laporan keuangan