I'm connected from a phone so it would be pretty hard to write out MY equation for An...here's the equation in words: square root of 3 over 4 + square root of 3 over 12 * ((9/5 -9/5(4/9)^n)... using your general expression for A_n and the iterative (what does that mean?) relation between A_n and A_n+1 already established, prove the general expression for A_n by induction? if you've read my previous post, I was looking for n when the value for the area (this relates to fractals) reaches a limit to the millionth decimal place, and I found it. at terms 17 (A_n+1) and 16 (A_n). now I'm confused, do not know how to prove my equation true without knowing the sum formula for the geometric sequence .