In this paper, the authors consider infinite sums derived from reciprocals of Fibonacci polynomials and Lucas polynomials. Then applying floor function to these sums, obtain several new identities involving MSC:11B39.

Let be a higher-order recursive sequence. Several identities are obtained for the infinite sums and finite of reciprocals sequences. MSC:11B39.

Abstract In this article, we consider infinite sums derived from the reciprocals of Fibonacci polynomials and Lucas polynomials, square polynomials. Then applying floor function to these sums, obtain several new equalities involving Mathematics Subject Classification (2010): Primary, 11B39.

<abstract><p>In this paper, we derive the asymptotic formulas $ B^*_{r, s, t}(n) such that</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \mathop{\lim} \limits_{n \rightarrow \infty} \left\{ \left( \sum\limits^{\infty}_{k = n} \frac{1}{k^r(k+t)^s} \right)^{-1} - B^*_{r,s,t}(n) \right\} 0, $\end{document} </tex-math></disp-formula></p> <p>where Re(r+s) > 1 and t \in \mathbb{C} $. It is evident that...

The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation if n even, odd, with initial values and , where a b are positive integers. In this paper, we consider reciprocal sum then establish some identities relating to denotes nearest integer x. MSC:11B39.

Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">{</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">}</mml:mo></mml:math>be a higher-order linear recursive sequence. In this paper, we use the properties of error estimation and analytic method to study reciprocal sums higher power sequences. Then establish several new interesting identities relating infinite finite sums.

Abstract In this paper, we use the properties of error estimation and analytic method to study reciprocal products bi-periodic Fibonacci sequence, Lucas m th-order linear recursive sequence.

&lt;abstract&gt;&lt;p&gt;In recent years, many mathematicians researched infinite reciprocal sums of various sequences and evaluated their value by the asymptotic formulas. We study formulas formed as $ \left(\sum^{\infty}_{k = n} \frac{1}{k^r(k+t)^s} \right)^{-1} for r, s, t \in \mathbb{N^+} $, where are polynomials.&lt;/p&gt;&lt;/abstract&gt;

&lt;abstract&gt;&lt;p&gt;In this paper, we considered the generalized bi-periodic Fibonacci polynomials, and obtained some identities related to polynomials using matrix theory. In addition, Lucas polynomial was defined by $ L_{n}\left (x \right) = bp\left L_{n-1}\left \right)+q\left \right)L_{n-2}\left (if n is even) or ap\left odd), with initial conditions L_{0}\left 2 $, L_{1}\left where p\left q\left were nonzero in Q \left [ x \right ] $. We a series of polynomials.&lt;/p&gt;&lt;/abstract&gt;

&lt;abstract&gt;&lt;p&gt;In this paper, by using generating functions for the Chebyshev polynomials, we have obtained convolution formulas involving bi-periodic Fibonacci and Lucas polynomials.&lt;/p&gt;&lt;/abstract&gt;

For any sequence recurrence formula, the Smarandache-Pascal derived of is defined by for all , where denotes combination number. The formula obtained properties third-order linear sequence.

&lt;abstract&gt;&lt;p&gt;In this paper, we use the method of error estimation to consider reciprocal sums products any $ m $th-order linear recurrence sequences \left \{ u_{n} \right \} $. Specifically, find that a series are "asymptotically equivalent" $.&lt;/p&gt;&lt;/abstract&gt;

The main purpose of this paper is, using the properties Gauss sums, estimate for character sums and analytic method, to study mean value two-term Dedekind give an interesting asymptotic formula it. MSC:11F20, 11L40.