Hard Proofs Question (2 Viewers)

[tickboom]

So I solved (v) with two applications of the Stolz–Cesàro theorem, I have given up on attempting a more within-the-syllabus proof.

Wow thanks so much! I will get Googling on the Stolz–Cesàro theorem and see if I can work it out. Agreed, I think this question is a beyond the syllabus.

 

[tickboom]

Wow thanks so much! I will get Googling on the Stolz–Cesàro theorem and see if I can work it out. Agreed, I think this question is a beyond the syllabus.

I finally found the time to work through this, and yes I was also able to work it out by applying the Stolz-Cesaro theorem twice. So glad to have finally solved this! For anyone interested in how to tackle this, you can see my working here:

 

[CM_Tutor]

I finally found the time to work through this, and yes I was also able to work it out by applying the Stolz-Cesaro theorem twice. So glad to have finally solved this! For anyone interested in how to tackle this, you can see my working here:

Very interesting, thanks for sharing.

I agree that Stolz-Cesaro is definitely well outside the syllabus.

I also note that the binomial theorem part is outside the syllabus as they only cover cases where n is a positive integer.

 

[tickboom]

Very interesting, thanks for sharing.

I agree that Stolz-Cesaro is definitely well outside the syllabus.

I also note that the binomial theorem part is outside the syllabus as they only cover cases where n is a positive integer.

Yes you're right. I misspoke when I referred to that as the binomial expansion. I should have said "binomial series" which is a power series that I definitely did not learn until university.