I am trying to solve a difference equation involving summation expression with the following code:

RSolve[{s[n + 1] - (s[n]*(Z/A)) == Sum[((1/A)*((1 - (F*L1))^(n - m))*(Q + (YY* s[m - 1]) - (PP*s[m]) + VV)), {m, 2, n}], s[0] == 0}, s[n], n]

where the capital letters show constant parameters. Mathematica gives a general solution which is very long and contains functions, such as DifferenceRoot in it. In fact, the equation is not solved completely. However, I need the closed-form for s[n].

Can anybody help me to find the closed-form solution? By the way, I want Mathematica to solve the difference equation starting at point 1, not at point 0. How can I code it with RSolve?
Many thanks.

  • $\begingroup$ Your code runs forever on Mathematica v12 Windows10/64! $\endgroup$ – Ulrich Neumann Aug 21 '20 at 8:20
  • $\begingroup$ Thank you for your kind remark. I think I need to consider 'n' initial conditions but I don't know how to do that when 'n' is not known. @UlrichNeumann $\endgroup$ – Mina Aug 22 '20 at 21:09

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