u/Jsample2

https://preview.redd.it/1myqocnj9wah1.png?width=1918&format=png&auto=webp&s=409ae449fdcd4edb6a1bf7face995ac8172839b0

Hello I need help with this problem. I've established that the sequence is increasing. I want to use the MCT that it is bounded --> this sequence is convergent.

I've tried using induction to show it's bounded above but it has not worked. I know this is related to the harmonic series that is divergent. I tried using a similar proof as in the book that used to establish that the harmonic series is divergent. I have not learned about series so I cannot use series properties here. I recognize that:

y_1 = 1/2 is less than or equal to 1/2

y_2 = 1/3 + 1/4 is less than or equal to 1/2 + 1/2 = 2/2 = 1

y_3 = 1/4 + 1/5 + 1/6 is less than or equal to 3/2 = 1.5

y_4 = 1/4 + 1/5 + 1/6 + 1/7 + 1/8 is less than or equal to 4/2 = 2

So y_n is less than or equal to n/2. . . How do I find a definite upper bound?

Thank you.

Hello,

I'm looking for a tutor in elementary real analysis.

I can't pay much, maybe $25-$35 per hour.

Once a week, evenings. My classes start mid june and I want to get ahead. I've already taken this class twice and failed before. Any help is appreciated. If you're also taking the same class this summer and would like to study together that would also be appreciated.

Thank you!

Hello,

I'm looking for a tutor in elementary real analysis.

I can't pay much, maybe $25-$35 per hour.

Once a week, evenings. My classes start mid june and I want to get ahead. I've already taken this class twice and failed before. Any help is appreciated. If you're also taking the same class this summer and would like to study together that would also be appreciated.

Thank you!

Hello,

I'm looking for a tutor in elementary real analysis.

I can't pay much, maybe $25-$35 per hour.

Once a week, evenings. My classes start mid june and I want to get ahead. I've already taken this class twice and failed before. Any help is appreciated. If you're also taking the same class this summer and would like to study together that would also be appreciated.

Thank you!