Keep a running product of the fixed base. In particular, 1.0/n uses floating-point arithmetic, avoiding the truncation that integer division would introduce:
def eaLinear(n: Int): Double = {
  require(n > 0)
  val base = 1.0 + 1.0 / n.toDouble
  var k = 0
  var result = 1.0
  while (k < n) {
    result *= base
    k += 1
  }
  result
}
The loop invariant is and . Initially the empty product is one. Multiplication by base and incrementing k preserve the invariant. The loop variant decreases by one. On exit , so the result is , with exactly multiplications and time complexity. With Double, the operational result is the rounded recurrence, rather than an exact real power; this distinction applies to the next two power computations too.

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