how do i write a matlab script to sum this expression?

Answer 1

[KSSV]

N = 100; 
thesum = 0 ;
for i = 1:N
    thesum = thesum+(1/i+1/((i+2)*(i+3))) ; 
end

Without Loop:

N = 100 ; 
f = @(i) (1./i+1./((i+2).*(i+3))) ; 
i = 1:N ; 
s = sum(f(i)) ; 

[JJD]

what does the "." for in the without loop script ?

[Stephan]

It is elementwise multiplication, so the calculation works in a vectorized way. This makes the code more efficient and no for loop is needed.

[JJD]

ohh, ok thank you

Answer 2

[Stephan]

Symbolic:

syms n positive integer
N = 10000;
eq = 1/n + 1/((n+2)*(n+3));
pretty(eq)
sol = symsum(eq,n,1,N)
sol_num = double(sol)

results in:

>> Untitled
       1          1
--------------- + -
(n + 2) (n + 3)   n

 
sol =
 
eulergamma + psi(10001) + 10000/30009
 

sol_num =

   10.1208

[JJD]

thank you, for your answer