http://img209.imageshack.us/my.php?image=14535404zm8.jpg http://img80.imageshack.us/my.php?image=34587054lt1.jpg this pictures have a high quality ,you can zoom it. in this links i show the question and how i tried to solve them. i was taught this convergence stuff using this type questions. i solve them like that --------------- a = (a +6)^0.5 n+1 n a1=(6)^0.5 n=>1 are given find if the goes up or down and if its converges and to what limit?? i know that An+1 and An has the same limit so i put L (limit) instead of them and get that there are two possible limits L=1 L=4 know i want to proove that this series goes up: i fing A2 using A1=(6)^0.5 A2=(11)^0.5 A2>A1 than using an inequality An+1>An (we assume that it is correct) i prooved An+2>An+1 and prooved that the function goes up than the same way i prooved than An<4 (converges to 4). but in this questions that i added in the link they dont follow this pattern i tried to solve them that way but they are different how do i solve them??