How Can I Solve Part B of This Series Problem?

[juanitotruan77]

Homework Statement

Well I am stuck with this math problem and i was wondering if you could help me:
https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-xfp1/v/t1.0-9/10997707_10200231195780272_1526570237911134602_n.jpg?oh=8d10e10d9c41470b751c36f4330864f1&oe=557F93B0&__gda__=1434457045_a894f47029b86afda4081e42d0282078
I already solved a), but i stuck with b)

2. The attempt at a solution
This is the solution i came up with for a)
https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xfp1/v/t1.0-9/14059_10200231203980477_4182850412301272757_n.jpg?oh=6182f6ae981b50b7a0642552a1f53f57&oe=554DBAB5&__gda__=1434983726_505d6a8220d0e1cc493cbdeffc88483e

Thanks in advance

 

[Dick]

Homework Statement

Well I am stuck with this math problem and i was wondering if you could help me:
https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-xfp1/v/t1.0-9/10997707_10200231195780272_1526570237911134602_n.jpg?oh=8d10e10d9c41470b751c36f4330864f1&oe=557F93B0&__gda__=1434457045_a894f47029b86afda4081e42d0282078
I already solved a), but i stuck with b)

2. The attempt at a solution
This is the solution i came up with for a)
https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xfp1/v/t1.0-9/14059_10200231203980477_4182850412301272757_n.jpg?oh=6182f6ae981b50b7a0642552a1f53f57&oe=554DBAB5&__gda__=1434983726_505d6a8220d0e1cc493cbdeffc88483e

Thanks in advance

Maybe I don't see the problem. But if $r_n$ is increasing up to a limit $L<1$, then isn't $\frac{1}{1-r_n} \le \frac{1}{1-L}$?

 

[juanitotruan77]

Maybe I don't see the problem. But if $r_n$ is increasing up to a limit $L<1$, then isn't $\frac{1}{1-r_n} \le \frac{1}{1-L}$?

That might be it, budd. Thanks. But i'd like to hear more suggestions, just in case.