[math-fun] another limit question

Everyone knows that the n-th triangular number squared is the sum of the first n cubes, but do you know that the n-th triangular number cubed divided by the sum of the first n fifth powers tends to 0.75? And also t(n)^4/sum of seventh powers tends to 0.5. And t(n)^5/sum of ninth powers tends to 5/16... t^6/sum_11 tends to 3/16, the next are 7/64 and 1/16, what is the general limit for t^k/sum_{2k-1}? Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com