Integrals and sums Although sums behave like integrals, because of the discrete

Question

Integrals and sums
Although sums behave like integrals, because of the discrete nature of the sums one needs to be careful with the upper and lower limits more than in the integral. To illustrate this, consider the separation of an integral into two integrals and compare them with the separation of a sum into two sums. For the integral, we have
Int: tdt with a = 0, b= 1
= int: tdt with a = 0, b = 0.5 + int: tdt with a = 0, b = 1
Show this is true by computing the three integrals. Then consider the sum
S = sum: n with 100, n = 0
Find this sum and determine which of the following is equal to this sum:
S1 = sum: n with 50, n = 0 + sum:n with 100, n = 50
S2 = sum: n with 50, n=0 + sum:n with 100, n = 51
Use symbolic MAATLAB function symsum to verify your answers.

Explanation / Answer

clear all clc syms x n int1=int(x,0,0.5) int2=int(x,0.5,1) int_all=int(x,0,1) disp('Therefore, int1+int2=int_all'); dt=1/100; S=symsum(n*dt*dt,n,0,100) S1=symsum(n*dt*dt,n,0,50)+symsum(n*dt*dt,n,50,100) S2=symsum(n*dt*dt,n,0,50)+symsum(n*dt*dt,n,51,100) disp('Therefore S2 is equation to the sum (S).');

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