Why summation and integrate give different results?

Question

I think I am misunderstanding something. I think that printed results of this code snippet must be equal, but they are not: import sympy x = sympy.Symbol('x') summation = sympy.summation(sympy.exp(-x), (x, 0, sympy.oo)) print(summation) # 1/(-exp(-1) + 1) integration = sympy.integrate(sympy.exp(-x), (x, 0, sympy.oo)) print(integration) # 1 Can you explain the difference between summation and integrate? JavaScript questions and answers, JavaScript questions pdf, JavaScript question bank, JavaScript questions and answers pdf, mcq on JavaScript pdf, JavaScript questions and solutions, JavaScript mcq Test , Interview JavaScript questions, JavaScript Questions for Interview, JavaScript MCQ (Multiple Choice Questions)

Answer 1

Nothing wrong. If you notice the summation is a sum of geometric sequence, you will find it to be different to integration. Summation: sum exp(-x) = sum exp(-1)^x = exp(-1)^0 / (1 - exp(-1)) = 1 / (1 - exp(-1)) Integration: int exp(-x) dx = - [ exp(-x) ] = - [ exp(-infinity) - exp(0) ] = - [ 0 - 1 ] = 1 Sorry. StackOverflow do not do LaTeX.