(Forgive the formatting)
// — Add a constant variable
public static final BigInteger BIG_INT_CONSTANT = BigInteger.valueOf(i);

/* the useful stuff */
private BigDecimal doCalculation()
{
BigInteger factorialTotal = new BigInteger(“1″);
BigDecimal bigE = new BigDecimal(“1″);

for (int i = 0; i < numberOfDigits; i++)
{
/*
* The Following adheres to the formula:
*
* e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + …
*
*/

// increment factorial by multiplying itself by itself
factorialTotal = factorialTotal.add(
factorialTotal.multiply(BIG_INT_CONSTANT));
// — ^^^^^^^^^^^^^ Use the constant variable
// e grows and becomes more accurate
bigE = bigE.add(
BIG_INT_CONSTANT.divide(new BigDecimal(factorialTotal), numberOfDigits, BigDecimal.ROUND_HALF_UP));
// — ^^^^^^^^^ Use the BigInteger parameter constructor

}

return bigE;
}