Sum Of Floor Series

Program to print arithmetic progression series.

Sum of floor series.

Definite integrals and sums involving the floor function are quite common in problems and applications. Sum of sum series of first n natural numbers sum of series formed by difference between product and sum of n natural numbers program to find sum of series 1 1 2 1 3 1 4. And floor n 2 2 floor n 2 1. Sum of elements of a geometric progression gp in a given range.

The best strategy is to break up the interval of integration or summation into pieces on which the floor function is constant. Evaluate 0 x e x d x. This is an application of the following fun result i published with natalio guersenzvaig a few years ago. The other piece in the puzzle is the expression for the sum of an arithmetic sequence which can be found here.

Int limits 0 infty lfloor x rfloor e x dx. Summation 8 formulas finite summation 7 formulas infinite summation 1 formula. Laguerre based hermite bernoulli polynomials associated with bilateral series ahmad khan waseem araci serkan acikgoz mehmet and esi ayhan tbilisi mathematical journal 2018 airflow and heat transfer in the slot vented room with radiant floor heating unit liu xiang long gong guang cai cheng heng sheng and ding li xing journal of. At points of continuity the series converges to the true.

Sum of product of x and y such that floor n x y. Assuming n is even then floor n 2 floor n 1 2. Sum d j 1 k lfloor n d rfloor sum d lfloor n k rfloor 1 lfloor n j rfloor lfloor n d rfloor k lfloor n k rfloor j lfloor n j rfloor this is corollary 4 in some inversion formulas for sums of quotients. 0 x.

Summation 8 formulas finite summation 7 formulas infinite summation 1 formula summation 8 formulas floor.