Hi mendhak,

It is because the -1 in step 3 is not part of the sum. For clarity it should be written: -1 + sum(1->n)[1/i].

Ways to tell:

1) You can test this fairly easily by bunging some numbers in.

2) The first sum is clearly 1/2 + 1/3 + ... + 1/n. The second is [1 + 1/2 + ... + 1/n] -1

3) If you want to prove it mathematically, do a substitution in the second sum of i = z+1. You then have sum(0->n-1)[1/{z+1}] -1
Evaluate the first term separately and you get:
1 + sum(1->n-1)[1/{z+1}] - 1 = sum(1->n-1)[1/{z+1}], which is what you had in the first place.


zaza