Re: [Maxima-discuss] Fail to understand result of funcsolve

[Robert D. <rob...@gm...>]

On Mon, Nov 24, 2025 at 12:15 PM Michel Talon <ta...@lp...> wrote:

> Package Zeilberger doesn't seem to allow to compute the sum.
>
> (%i16) GosperSum((%j+1)*(%j+2)/%j,%j,1,n-1);
> (%o16)                        NON_GOSPER_SUMMABLE

For the record, the package simplify_sum (which makes use of Gosper's
and Zeilberger's algorithms and others) returns the following result.

(%i2) load (simplify_sum) $
(%i3) sum ((%j+1)*(%j+2)/%j,%j,1,n-1);
(%o3) 'sum(((%j+1)*(%j+2))/%j,%j,1,n-1)
(%i4) simplify_sum (%);
(%o4) (n+(n-1)^2-1)/2+3*(n-1)+2*harmonic_number(n-1)

which seems plausible, although I didn't check it.

best,

Robert