Incompatible Array Size/Mathematical Input Error

I was trying to get the "exact" function to work its rather long though, and I've typed it all out below in MATLAB.

For the exact equation I really don't know how I shoud even input the summation, since I've never worked with one like that before, so I suspect I've done that wrong or maybe I misinterperated the instuctions? But If anyone sees what I've done wrong I'd really appriciate it.

So far, I've typed everything in as follows:

clear;clc
x = 3.*[8 7 4];
V = [8 7 4];
R = [8 7 4];
Eo = V./(2.*R);
r = ((2.*R) + x)./(2.*R);
B = acosh(r);
n = 1:100;
S = x./(2.*R);
f = ((1./sinh(2.*n.*B)).*(1+r+(sinh(B).*((coth(2.*n.*B))))./(1-r-(sinh(B).*(coth(2.*n.*B)))).^2)+(cosh(2.*B))+r+(((2.*r)+1).*(sinh(B).*((coth(2.*n.*B)))))./(((cosh(2.*B))-r-(((2.*r)-1).*(sinh(B).*((coth(2.*n.*B)))))).^2));

Arrays have incompatible sizes for this operation.

E_max_simp = (Eo./4.*S).*(1+(2.*S)+sqrt((1+(2.*S)).^2)+8);
E_max_exac = Eo(1+((2.*r+1)/(2.*r-1)^2))+sinh(B).*syssum(f,n,1,inf);

Answer 1

[Walter Roberson]

x = 3.*[8 7 4];
V = [8 7 4];
R = [8 7 4];
Eo = V./(2.*R);
r = ((2.*R) + x)./(2.*R);
B = acosh(r);
syms m n integer
S = x./(2.*R);
E_max_simp = (Eo./4.*S).*(1+(2.*S)+sqrt((1+(2.*S)).^2)+8)

E_max_simp = 1×3

3 3 3

f = ((1./sinh(2.*n.*B)).*(1+r+(sinh(B).*((coth(2.*n.*B))))./(1-r-(sinh(B).*(coth(2.*n.*B)))).^2)+(cosh(2.*B))+r+(((2.*r)+1).*(sinh(B).*((coth(2.*n.*B)))))./(((cosh(2.*B))-r-(((2.*r)-1).*(sinh(B).*((coth(2.*n.*B)))))).^2));

E_max_exac = Eo .* (1+((2.*r+1)/(2.*r-1).^2))+sinh(B).*symsum(f,n,1,m);
E_max_exac_100 = vpa(subs(E_max_exac, m, 100))

E_max_exac_100 = 

Notice that your E_max_simp is constant. Notice that your Eo is a vector that has all entries work out to exactly 1/2, and notice that your E_max_simp does not involve n or any sum.. everything happens to cancel out leaving constants.