# Problem in finding out the root of the equation with sums

Posted 8 years ago
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 I am facing the problem in finding out the root of the equation. Feedback is appreciated. Attachments:
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Posted 8 years ago
 Perhaps use Simplify to handle the denominators. In[1]:= Clear[m, k, l, a, b, A, B]; simp = Simplify[1/Sum[Binomial[m-k, l]*(-1)^l*Gamma[k+a]/( b + B + k/A^2)^(k+a), {l, 0, m-k}]* Sum[Binomial[m-k, l]*(-1)^l*Gamma[k+a]/(1/L^2 + b + B + k/A^2)^(k+a), {l, 0, m-k}]]; m = 35; k = 32; \[Lambda] = 1; a = 2; b = 2; u = RandomReal[UniformDistribution[{0, 1}], m]; t = ((-1*\[Lambda])/Log[u])^(1/2); s = t; w = Sort[s]; st = Take[w, k]; B = Total[st^-2]; A = Last[st]; FindRoot[simp == 0.25, {L, 1}] FindRoot[simp == 0.75, {L, 1}] Plot[{simp - 0.25, simp - 0.75}, {L, 0, 3}] Out[4]= {L -> 0.72545} Out[5]= {L -> 1.60547} Please check this carefully. Thank you
Posted 8 years ago
 The cover posting for a notebook should include a summary of the problem and a clear question. In this case, both of the Sums add to zero so your equation is 0/0 == 0.25. It may be that the limits on the sums are not correct. Please try evaluating pieces of the equation separately to find where it goes astray. Moderation Team