^
n+(3-sqrt(8))^
n)/2;
//n=nombres de termes et a fonction definissant a(n) //S_n(P_n) =seriealt(n,a) //S_n(P_n) approche sum((-1)^k*a(k),k,0,+infinity) //avec P_n=poly de chebyshev seriealt1(n,a):={ local k,d,c,p,S; d:=((3+sqrt(8))^n+(3-sqrt(8))^n)/2; p:=1; c:=d-p; S:=a(0)*c; for (k:=1;k<n;k++) { p:=p*(k+n-1)*(k-n-1)/(k-1/2)/k; c:=-p-c; S:=S+a(k)*c; } return evalf(S/d); };