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The infinite sum of reciprocal pell numbers

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 https://primechaletsolutions.com

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

List of sums of reciprocals - Wikipedia

Category:On the Sum of Reciprocal Generalized Fibonacci Numbers - Hindawi

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The infinite sum of reciprocal pell numbers

On the reciprocal sums of the generalized Fibonacci sequences

Webnumbers and the infinite sums of reciprocal generalized Fibonacci sums. Applying the floor function to the reciprocals of these sums, our results generalize some identities of Holliday and Komatsu and extend some results of Liu and Zhao. 1 Introduction Let a,bbe two positive integers and cnon-negative integer. Define the generalized ... WebThis was proved by Leonhard Euler in 1737, and strengthens Euclid's 3rd-century-BC result that there are infinitely many prime numbers and Nicole Oresme's 14th-century proof of the divergence of the sum of the reciprocals of the integers (harmonic series).. There are a variety of proofs of Euler's result, including a lower bound for the partial sums stating that

The infinite sum of reciprocal pell numbers

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WebIn [18], Xu and Wang applied the method of undetermined coefficients and constructed a number of delicate inequalities in order to study the infinite sum of the cubes of reciprocal Pell numbers and then obtained the following meaningful result. Proposition 2. WebThe sum of the reciprocals of the numbers in any sum-free sequence is less than 2.8570. …

WebJun 27, 2013 · Ohtsuka and Nakamura [ 3] studied the partial infinite sums of reciprocal Fibonacci numbers and proved the following conclusions: ⌊ ( ∑ k = n ∞ 1 F k ) − 1 ⌋ = { F n − 2 if n is even and n ≥ 2 ; F n − 2 − 1 if n is odd and n ≥ 1 . ⌊ ( ∑ k = n ∞ 1 F k 2 ) − 1 ⌋ = { F n − 1 F n − 1 if n is even and n ≥ 2 ; F n − 1 F n if n is odd and n ≥ 1 . WebOn the reciprocal sums of generalized Fibonacci numbers. Y. Choo. Mathematics. 2016. In …

WebOct 12, 2024 · In this paper, the infinite sums of reciprocals and the partial sums derived … WebApr 1, 2024 · The infinite sum \sum^ {\infty}_ {k=1}\frac {1} {f_ {k}} is known to be irrational, but it is unknown whether \sum^ {\infty}_ {k=1}\frac {1} {f_ {k}^ {2}} is irrational or not. Reciprocal sum of f_ {k}^ {2} In [ 6 ], Ohtsuka and Nakamura proved the …

WebMar 15, 2013 · In 2013, Kiliç and Arikan [22] studied a problem which differs slightly from the one in [7], namely, they determined the nearest integer to (∑ ∞ k=n (1/u k )) −1 . Specifically, suppose that x = x...

WebJan 15, 2012 · Introduction. For any integer n ⩾ 0, the famous Pell numbers Pn are defined … bank rbassWebMore on the infinite sum of reciprocal Fibonacci, Pell and higher order recurrences. More … bank raya rupsWebApr 13, 2024 · It is currently difficult to match banks so that all are able to offer such high limits (most offer just a few million dollars' insurance), and reciprocal-deposit firms levy fees, too. They apply on top of the charges, of between 0.05% and 0.32% of the value of total liabilities, that institutions pay for federal-deposit insurance. bank raya semarang