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Error Sympy series summation

Time:11-23

As shown In figure, a series, a substitute 1 In fantasy, after x 0.5 instead, In the [85] In numerical calculation, and keep the three significant figures, results In the imaginary part!
Series of each item is real, and finally sympy gives the results of the imaginary part is bound to have problems, and the series was actually (absolute, consistent) convergence, supposedly for numerical computation is no problem, so it is very confused,
For help, why sympy calculation results become so, if you want to get the correct result, how to solve,
After another: a substitute 1 from the expr, use sympy. Lambdify into a normal function, but to this function into a concrete value would be an error, at the same time, if to increase the effective number of evalf to 4 and above, program error (hint Nan values cannot compare)
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