Convergence of p-series revisited with applications
نویسندگان
چکیده
Theorem 2 is the main result in this note. Lemma 1 is key to our main result. It is different from the result in [2] because it does not restrict the number of terms in the partial sum to an even one. Also, our inequalities (2) should be compared with the corresponding result in [2] for k = 2. Lemma 1. Let sn(p) be the nth partial sum of the p-series ∑∞ i=1(1/i), and let k be any integer greater than 1. (a) If p > 0, then sk−1(p)− k− 1 kp + k kp sn(p) < skn(p) < sk−1(p) + k kp sn(p). (1)
منابع مشابه
Non-Newtonian Fuzzy numbers and related applications
Although there are many excellent ways presenting the principle of the classical calculus, the novel presentations probably leads most naturally to the development of the non-Newtonian calculus. The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Since this self-contained work is intended for a wide audience, inc...
متن کاملImpedance Control of Robots Using Voltage Control Strategy Revisited
In this note, we show that the impedance control strategy proposed in the paper is not feasible from practical implementation point of view. Next, a robust impedance controller is proposed for electrically driven robots using Fourier series (FS). The fact that robots' actuators have limited voltage is also considered in controller design procedure. In comparison with other impedance controllers...
متن کاملHigh level Ab inito bench mark computaions on weak interactions (H2)2 dimer revisited
The Potential Energy Surface PES of (H2)2 dimer has been investigated, using five simple rigid rotor models. These models are called: head to head, symmetric side to side, L , steplike and T model. All calculations were done at two levels of ab initio methods: MP2(Full) and QCISD (T,Full) using cc-pVTZ basis set at singlet state of spin multiplicity. The results of scanning PES were then fitte...
متن کاملStrong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings
In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space with a uniformly G$hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(ell_{p})$ spaces, $1 < p
متن کاملOn convergence of homotopy analysis method to solve the Schrodinger equation with a power law nonlinearity
In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2006 شماره
صفحات -
تاریخ انتشار 2006