Originally Posted by

**PvtBillPilgrim** Could someone just tell me if the following sequences converge or not:

Let an = the summation of (1/x) beginning with x = n+1 and ending with 2n.

For example, if n =2, x =3, then the sequence is (1/3) + (1/4).

Let bn = the summation of (1/x) beginning with x = n+1 and ending with pn where p is a positive integer greater than one.

For example, if n =2, x =3, and p =3, then the sequence is (1/3) + (1/4) + (1/5) + (1/6).

It seems to me that both sequences are increasing and bounded above, which would make them convergent. Is this true or not?