Subject: summation problem My name is otoniel. The level of the problem is precalculus. Here it is: Without using mathematical induction, or any other method discovered after 1010 a.d. , prove that the sum of i^{3}, (where i, is the index of summation) from one to, n, is equal to ((n*(n+1))/2)^{2}. Hi Otoniel,I am not sure what exactly you are able to use but I can point you in the direction of a proof that does not use mathematical induction. First you need to know that for each positive integer k Next consider the (1+2+3+...+n) by (1+2+3+...+n) square and find the area of each of the Lshaped regions. Cheers,Penny
