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In this paper, we examine the nonlinear Weakly Singular Volterra Integral Equation(WSVIE), u(x)=f(x)+_0^xt^μ-1 x^μ[u(t)]^β dt. AL-Jawary and Shehan used Daftardar-Jafari Method(DJM) and solved the above integral equation for the investigation parameter μ>1 using specific force functions with μ and β values and obtained unique solutions. We have discovered a force function f(x)=x^k_1-x^γ k_1 γ k_1+μ , that allows the introduction of noise terms phenomena discovered by Wazwaz; that cancel out the terms of the power series in the successive solution terms u_m, m=0,1,2,...,n: we thus obtain a maximum finite power series terms for each solution term called truncation point and denoted by x^g(n). Such that the integral solution can be written as u(x)=u_0+_m=1^nu_m, where n is finite. Simplifying the solution terms we get the unique solution u(x)=x^k_1, irrespective of n-value in the truncation point. We discovered a formula relation between the last solution term u_n and the truncation point as u_n=a_nx^g(n). Our results confirm the results of the two solution examples of AL-Jawary and Shehan for the investigation parameter μ>1. We extend the parameter range to include μ>1 and 0<μ≤ 1 for our solution. In addition, for any chosen rational parameter k_1, the solution u(x)=x^k_1 is extrapolated to be valid for all integer parameter values β≥ 2, and positive rational parameter value μ>0 and for any finite value of n≥2. , number=2, journal=European Journal of Pure and Applied Mathematics, year=2024, month=Apr., pages=1046–1069