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create a sequence symbolically and then find a series based on this sequence

asked 2019-05-31 11:27:32 +0100

Tintin gravatar image

I would like to create an infinite sequence (a_o,a_1,a_2,...) symbolically and then find an infinite series sum(a_0+a_1z+a_2z+...) based on this sequence with the coefficients based n the initial symbolical sequence. After that I would like to manipulate this sequence further. I am rather new to Sagemath. How can this be done? Thanks

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answered 2019-05-31 14:50:05 +0100

tmonteil gravatar image

updated 2019-05-31 14:52:02 +0100

If you want a precise answer, you should provide more details about your actual sequence. Otherwise, here is a generic example:

sage: var('n')
sage: a(n) = 1/n^2 + 1/n^3
sage: a
n |--> 1/n^2 + 1/n^3
sage: sum(a,n,1,infinity)
1/6*pi^2 + zeta(3)
sage: a(n) + a(n + 1)
1/(n + 1)^2 + 1/n^2 + 1/(n + 1)^3 + 1/n^3
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Asked: 2019-05-31 11:27:32 +0100

Seen: 244 times

Last updated: May 31 '19