The length of triangle base is 26. a line, which is parallel to the base divides the triangle into two equal area parts. find the length of the segment between triangle legs.
Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. 1^2 + 4^2 + 7^2 + + (3n - 2)^2 = [n(6n^2-3n-1)/2]