Math Is Fun Forum

MarvinRayBurns

Member

Registered: 2011-01-09

Posts: 15

Special partial sums

For all real a, the partial sums s(n)= sum((-1)^k (k^(1/k) -a), k=1..n) are bounded so that their limit points form an interval [-1.+  the MRB constant +a, MRB constant] of length 1-a, where the MRB constant is limit(sum((-1)^k*(k^(1/k)), k = 1 ..2*N),N=infinity).

For all complex z, the upper limit point of  sn= sum((-1)^k (k^(1/k) -z), k=1..n) is the  the MRB constant.

Last edited by MarvinRayBurns (2014-09-14 09:08:59)