0o The series (n- 1 )! converges to the number e. (This is given information. n= 1 You do not need to prove this, but we may be able to prove it before the end of the course.) Compute S1, S2, S3, S4, ...... by adding the first several terms of the series. Notice that for each additional term you add, the sum is closer and closer to e. What is the smallest /V such that Sy gives an approximation of the number e that is correct to 3 decimal places? Side note: Some calculators do computations involving e, 7, sin (0.3) and many other transcendental numbers by using sums of series such as the one above (although recently there are also faster methods that calculators can use)