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Question: Finite series contradictory results

Question:Finite series contradictory results

tsunamiBTP 292 Maple 12
series
May 12 2012
0

Attached are results I obtained in MAPLE 12.  Can anyone explain the contradiction?

In short, if I sum from n = 0 to some integer I get a FALSE when testing the equality, which is what I would EXPECT.  However, if I change the integer to a variable to represent that integer such as m--> the result is TRUE?

Note the change in the variable of beta to alpha inside the series expression within the parentheses.

regards

sum(exp(-(2*I)*Pi*f*n*T)*(1/f-(f-I*beta*F)/(sqrt(1-beta^2)*(f^2-(2*I)*f*beta*F-F^2)))/((2*I)*Pi), n = 0 .. m)-exp(-(2*I)*Pi*f*(n+1)*T)/((2*I)*Pi*f) = sum(exp(-(2*I)*Pi*f*n*T)*(1/f-(f*(f^2-F^2+2*F^2*alpha^2)+I*alpha*F*(F^2+f^2))/(sqrt(1-beta^2)*((F-f)^2*(F+f)^2+4*f^2*alpha^2*F^2)))/((2*I)*Pi), n = 0 .. m)-exp(-(2*I)*Pi*f*(n+1)*T)/((2*I)*Pi*f)
(->)true

sum(exp(-(2*I)*Pi*f*n*T)*(1/f-(f-I*beta*F)/(sqrt(1-beta^2)*(f^2-(2*I)*f*beta*F-F^2)))/((2*I)*Pi), n = 0 .. 2)-exp(-(2*I)*Pi*f*(n+1)*T)/((2*I)*Pi*f) = sum(exp(-(2*I)*Pi*f*n*T)*(1/f-(f*(f^2-F^2+2*F^2*alpha^2)+I*alpha*F*(F^2+f^2))/(sqrt(1-beta^2)*((F-f)^2*(F+f)^2+4*f^2*alpha^2*F^2)))/((2*I)*Pi), n = 0 .. 2)-exp(-(2*I)*Pi*f*(n+1)*T)/((2*I)*Pi*f)
(->)false

sum(exp(-(2*I)*Pi*f*n*T)*(1/f-(f-I*beta*F)/(sqrt(1-beta^2)*(f^2-(2*I)*f*beta*F-F^2)))/((2*I)*Pi), n = 0 .. 1)-exp(-(2*I)*Pi*f*(n+1)*T)/((2*I)*Pi*f) = sum(exp(-(2*I)*Pi*f*n*T)*(1/f-(f*(f^2-F^2+2*F^2*alpha^2)+I*alpha*F*(F^2+f^2))/(sqrt(1-beta^2)*((F-f)^2*(F+f)^2+4*f^2*alpha^2*F^2)))/((2*I)*Pi), n = 0 .. 1)-exp(-(2*I)*Pi*f*(n+1)*T)/((2*I)*Pi*f)
(->)false

sum(exp(-(2*I)*Pi*f*n*T)*(1/f-(f-I*beta*F)/(sqrt(1-beta^2)*(f^2-(2*I)*f*beta*F-F^2)))/((2*I)*Pi), n = 0 .. infinity)-exp(-(2*I)*Pi*f*(n+1)*T)/((2*I)*Pi*f) = sum(exp(-(2*I)*Pi*f*n*T)*(1/f-(f*(f^2-F^2+2*F^2*alpha^2)+I*alpha*F*(F^2+f^2))/(sqrt(1-beta^2)*((F-f)^2*(F+f)^2+4*f^2*alpha^2*F^2)))/((2*I)*Pi), n = 0 .. infinity)-exp(-(2*I)*Pi*f*(n+1)*T)/((2*I)*Pi*f)
(->)false``

sum(exp(-(2*I)*Pi*f*n*T)*(1/f-(f-I*beta*F)/(sqrt(1-beta^2)*(f^2-(2*I)*f*beta*F-F^2)))/((2*I)*Pi), n = 0 .. 0)-exp(-(2*I)*Pi*f*(n+1)*T)/((2*I)*Pi*f) = sum(exp(-(2*I)*Pi*f*n*T)*(1/f-(f*(f^2-F^2+2*F^2*alpha^2)+I*alpha*F*(F^2+f^2))/(sqrt(1-beta^2)*((F-f)^2*(F+f)^2+4*f^2*alpha^2*F^2)))/((2*I)*Pi), n = 0 .. 0)-exp(-(2*I)*Pi*f*(n+1)*T)/((2*I)*Pi*f)
(->)false

``


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