oo ==== 2 2 \ 3 k + (3 a + 1) k + a > --------------------------------- = 1, / 2 k + a + 1 ==== (k + a) (k + a + 1) ( ) k = 0 k
It is interesting that Maple can do the second one,
Likewise (my, at least) Macsyma. But DUH! I'm getting senile. I thought and then forgot to check: That sum merely telescopes. Telescoping series have no need of "termination to the left" (or the right).
but for the first one gives the following answer,
sum((n + a)*(11*n + 6*a + 1)*4^n*(n + a - 5/6)!*(n + 2*a - 2)!*(2*n + a - 1)!/(n + a - 2/3)!/(3*n + 2*a + 1)!,n=0..infinity);
/ 16 7/360 (1/6)! |60 hypergeom([1/2, 1, 1, 7/6], [4/3, 4/3, 5/3], --) \ 27 ...
That did a nicer job than Macsyma, but I strongly object to the gratuitous change of notation from sum to hypergeom. In Macsyma, you say makehyper, or make1hyper if you want a single one. --rwg Henry> Is there a "no man's land", where neither the CA nor the NV
highway patrol will give tickets?
More likely it's where *both* highway patrols will get you.