How can I resolve the insufficient memory to complete the computation problem for solving function with iterated variables?

Question

I am trying to solve for a value x in a function where the variables varies with iterations of K. Also, there is one variable called "rvsum" which is updated with a certain formula as well. I have created the formula but it shows the error saying insufficient memory to complete the computation.. The code that I am struggling to get the solution is the following:

 rvsum1[1] = 5320007.301;
 rvsum1[i + 1] := 
 rvsum1[i] + (UT1[[i + 1]]*RA1[[i + 1]] - UT1[[i]]*RA1[[i]])^2;

 rp[i]:=((rvsum1[i]+((UT1[[i+1]]+x)*RA1[[i+1]]-UT1[[i]]*RA1[[i]])^2)/MM1[[i]])^(1/2)

  Table[x /. 
  Solve[-4*x* RA1[[K]] + 
    Sqrt[dt] *
     Z[[K]] (( 
       RA1[[K + 1]] (RA1[[K + 1]]*(x + UT1[[K + 1]]) - 
          RA1[[K]] *UT1[[K]]))/(
       MM1[[K]]*rp[K]))/(4*x*a1[[K]] + 
        0.5*4*x*4*
         x*\L[[K]] - (-4*x* RA1[[K]] + 
          Sqrt[dt] *
           Z[[K]] ( 
            RA1[[K + 
               1]] (RA1[[K + 1]]*(x + UT1[[K + 1]]) - 
                RA1[[K]] *UT1[[K]])/(MM1[[
                K]]* \[Sqrt](1/
                MM1[[K]] (rvsum1[
                K] + (RA1[[K + 1]]*(x + UT1[[K + 1]]) - 
                RA1[[K]] *UT1[[K]])^2)))))) - (MU[[
       K + 1]]/(rp[K] - MU[[K + 1]])) == 0, x][[1]], {K, 1, 10}] //
       Simplify // N

The values for the double brackets are all already available. I know the code is quite long but this is the only way that I can get my desired result. Is there a way to resolve this insufficient memory to complete the computation since I cannot even get the values that I need? If I am wrong with my code, I may try to fix it, but since it is the matter of insufficient memory to complete the computation issue, I am not even able to do that work at all.. Thank you very much in advance.

Answer 1

Ok, here you have it, but in the future this kind of questions will most likely be closed because the main problem arises from very basic errors. You can't expect others do the debugging for you. Take a look at the functions' definitions.

{UT1, RA1, MM1, Z, MU, a1, L} = Transpose[RandomReal[{0, 1}, {10, 7}]];
dt = 1;
rvsum1[1] = 5320007.301;
rvsum1[i_] :=  rvsum1[i - 1] + (UT1[[i]]*RA1[[i]] - UT1[[i - 1]]*RA1[[i - 1]])^2

rp[i_] := ((rvsum1[i] + ((UT1[[i + 1]] + x)*RA1[[i + 1]] - UT1[[i]]*RA1[[i]])^2)/ MM1[[i]])^(1/2)

Table[x /. 
  FindInstance[-4*x*RA1[[K]] +  Sqrt[dt]* Z[[K]] ((RA1[[K + 1]] (RA1[[K + 1]]*(x + UT1[[K + 1]]) - 
               RA1[[K]]*UT1[[K]]))/(MM1[[K]]*rp[K]))/(4*x*a1[[K]] + 0.5*4*x*4*x* L[[K]] - 
               (-4*x*RA1[[K]] + Sqrt[dt]* Z[[K]] (RA1[[K + 1]] (RA1[[K + 1]]*(x + UT1[[K + 1]]) - 
               RA1[[K]]* UT1[[K]])/(MM1[[K]]*[Sqrt](1/ MM1[[K]] (rvsum1[
                    K] + (RA1[[K + 1]]*(x + UT1[[K + 1]]) - 
                    RA1[[K]]*UT1[[K]])^2)))))) - (MU[[K + 1]]/(rp[K] - MU[[K + 1]])) == 0, x], 
{K, 2, 5}]

(*  {{-0.513926}, {-0.468765}, {-0.328148}, {-1.49684}} *)