prove that:

sqrt(1 + 2sqrt(1 + 3sqrt(1 +...))) = 3

i am not sure how to start this. the only thing i can think of is squaring both sides:

1 + 2sqrt(1 + 3sqrt(1 + 4sqrt(1 +...))) = 9

sqrt(1 + 3sqrt(1 + 4sqrt(1 + 5sqrt(1 +...)))) = 4

and so on. im not sure if this is the right way going about this. any hints?