(R) Implementing a program which solves lower triangular systems

Question

I have to write a program which takes a lower triangular matrix L and a vector b as input, and a solution x as output.

So first I computed a trivial program which only can handle 3x3 triangular matrices.

L3solve <- function(L,b) {
   b[1] <- b[1] / L[1,1]
   b[2] <- (b[2] - L[2,1]*b[1]) / L[2,2]
   b[3] <- (b[3] - L[3,1]*b[1] - L[3,2]*b[2]) / L[3,3]
   return(b)
  } 

After that I made a generalized version of it:

Lsolve <- function(L,b) {
    b[1] <- b[1] / L[1,1]
    for(i in 2:nrow(L)) {
        b[i] <- (b[i] - sum(L[i,i-1]*b[i-1])) / L[i,i]
    }
    return(b)
}

But this version doesn't work. Can anybody tell me what I'm doing wrong?