`SequenceLimit` became `NumericalMath``NSequenceLimit`. In the past, that change broke some of the examples on `NLimit` that used `SequenceLimit`. I reported the breakage, and the examples were fixed to use the same syntax but not actually call the now-non-existent function. The only remaining reference in the documentation that I can find to the use of `SequenceLimit` ***as if it were still a function*** is on the last bullet point of `NLimit`'s detailed description for its `Method` option: "uses `SequenceLimit` on constructed sequence". Recently, I started investigating the behavior of `NumericalMath``NSequenceLimit` because I need it in my engineering work. I feel `NumericalMath``NSequenceLimit` has some quite confusing shortcomings in regard to the approximation it returns vs. the number of terms supplied, so I wrote my own version [from][1] [some][2] [references][3]. A comparison appears below showing the convergence of partial sums of series approximations to `Pi` and `E`. Afterward, I use symbolic lists to document several parts of `NumericalMath``NSequenceLimit` that seem... possibly wrong... to me. sPi@n_:=Sum[4(-1)^nn/(2nn+1),{nn,0,n}]; Table[sPi@n,{n,0,4-1}]//N (*{4.,2.66667,3.46667,2.89524}*) NumericalMath`NSequenceLimit@% (*3.16667*) sequenceLimit@%% (*3.13333*) (*my answer is closer to Pi~=3.141, for good reason as shown below in the general case with 4 terms {a,b,c,d}*) sE@n_:=Piecewise[{{(1+1/n)^n ,n!=0}},1] Table[sE@n,{n,0,4-1}]//N (*{1.,2.,2.25,2.37037}*) NumericalMath`NSequenceLimit@% (*2.33333*) sequenceLimit@%% (*2.48214*) (*my answer is closer to E~=2.71828, for good reason as shown below in the general case with 4 terms {a,b,c,d}*) Below, I illustrate the difference between the behavior of the built-in `NumericalMath``NSequenceLimit` function vs. my `sequenceLimit` function for symbolic lists, like `{a,b,c,d}`. Quiet@NumericalMath`NSequenceLimit[{a,b,c}] (*NumericalMath`NSequenceLimit[{a,b,c}]*) (*yes, unevaluated with 3 inputs*) sequenceLimit[{a,b,c}]//Simplify (*my function*) (*(-b^2+a*c)/(a-2*b+c)*) (*same as Mathematica's next result with 4 inputs*) NumericalMath`NSequenceLimit[{a,b,c,d}] (*(-b^2+a*c)/(a-2*b+c)*) (*yes, only references a, b, & c not the later, more converged, d*) sequenceLimit[{a,b,c,d}]//Simplify (*my function*) (-c^2+b*d)/(b-2*c+d) (*note use of d, which explains why my approximations for Pi and E above are better*) Quiet@NumericalMath`NSequenceLimit[{a,b,c,d,e}]//Simplify (*(-b^2+a*c)/(a-2*b+c)*) (*yes, same result as with 4 terms, no d or e in output*) sequenceLimit[{a,b,c,d,e}]//Simplify (*my function*) (*(c^3+a*d^2+b^2*e-c*(2*b*d+a*e))/ (b^2+3*c^2-2*c*d+d^2-2*b*(c+d-e)-c*e-a*(c-2*d+e))*) (*note use of d and e*) I also document some error messages that seem spurious. NumericalMath`NSequenceLimit[{a}] (*NumericalMath`NSequenceLimit::seqw Sequence of length 1 is too short for use with Degree -> 1*) (*NumericalMath`NSequenceLimit::bdmtd WynnEpsilon is not a valid specification of a sequence limit extrapolation algorithm.*) (*NumericalMath`NSequenceLimit[{a}]*) NumericalMath`NSequenceLimit[{a},Degree->1]; (*Nulled output*) (*NumericalMath`NSequenceLimit:optx Unknown option ° in NumericalMath`NSequenceLimit[{a}]*) NumericalMath`NSequenceLimit[{a},"Degree"->1]; (*Note quotes*) (*NumericalMath`NSequenceLimit::optx Unknown option "Degree" in NumericalMath`NSequenceLimit[{a}]*) sequenceLimit[{a}] (*sequence limit is my function*) (*a*) Quiet@NumericalMath`NSequenceLimit[{a,b}] (*NumericalMath`NSequenceLimit[{a,b}]*) sequenceLimit[{a,b}] (*my function*) (*b*) Everything above is from the current version of Mathematica Online. $Version 11.3.0 for Linux x86 (64-bit) (March 7, 2018) Here is the definition of my function wynnE[-2,_,_]:=0 wynnE[-1,n_,s_]:=s@n wynnE[rkp1_,n_,s_]:= wynnE[rkp1-2,n+1,s]+1/(wynnE[rkp1-1,n+1,s]-wynnE[rkp1-1,n,s]) sequenceLimit[list_?VectorQ]:= With[{len=Length@list}, With[{rList=If[OddQ@len,list,Rest@list]}, wynnE[Length@rList-2,0,rList[[#+1]]&] ]/;len>0 ] [1]: http://mathworld.wolfram.com/WynnsEpsilonMethod.html [2]: http://www.adamponting.com/wynns-epsilon-method/ [3]: http://www.dtic.mil/dtic/tr/fulltext/u2/a109445.pdf