Zach P.
asked • 11/02/23I can not figure out how to find the exact sum of series, and I can't find much information online.
The question is:
Find the exact sum of the series
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2 Answers By Expert Tutors
Since an=2/(x^2+7x+1) is NOT a function of n, the series will not converge for any value of x, thus there is no exact sum.
Bradford T. answered • 11/03/23
Tutor
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Retired Engineer / Upper level math instructor
Convert summation to lim n→∞ ∑n1 () = ∫ ∞1()dx and solve using partial fraction decomposition.
Kevin S.
tutor
Isn't this only an approximation? Or are you talking Riemann sums?
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11/03/23
Mark M.
The denominator is prime. How can partial fraction decomposition be achieved?
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11/03/23
Doug C.
Partial fraction decomposition can be achieved, but the result is not pretty. And, the result does not give a telescoping series. My guess is the post should have shown the denominator as n^2 + 7n + 10? So far no response from the poster. desmos.com/calculator/6lx6nggj9a
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11/04/23
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Doug C.
Is this really intended as n=1 with x's only in the summation? Or should the variables be the same?11/03/23