code: def test_gosper_sum_iterated():
      f1 = binomial(2 * k, k) / 4**k
      f2 = (1 + 2 * n) * binomial(2 * n, n) / 4**n
      f3 = (1 + 2 * n) * (3 + 2 * n) * binomial(2 * n, n) / (3 * 4**n)
      f4 = (
          (1 + 2 * n)
          * (3 + 2 * n)
          * (5 + 2 * n)
          * binomial(2 * n, n)
          / (15 * 4**n)
      )
      f5 = (
          (1 + 2 * n)
          * (3 + 2 * n)
          * (5 + 2 * n)
          * (7 + 2 * n)
          * binomial(2 * n, n)
          / (105 * 4**n)
      )
  
      assert gosper_sum(f1, (k, 0, n)) == f2
      assert gosper_sum(f2, (n, 0, n)) == f3
      assert gosper_sum(f3, (n, 0, n)) == f4
      assert gosper_sum(f4, (n, 0, n)) == f5
  
imports: from sympy.core.numbers import Rational, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol
  from sympy.functions.combinatorial.factorials import binomial, factorial
  from sympy.functions.elementary.exponential import exp, log
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.special.gamma_functions import gamma
  from sympy.polys.polytools import Poly
  from sympy.simplify.simplify import simplify
  from sympy.concrete.gosper import gosper_normal, gosper_sum, gosper_term
  from sympy.abc import a, b, j, k, m, n, r, x
label_desc: Use image node_id 7 for calling a global function with example usage: test_gosper_sum_iterated() without return types