How to Prove that the Limit of (2n + 1)/(3n + 7) as n approaches infinity is 2/3

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How to Prove that the Limit of (2n + 1)/(3n + 7) as n approaches infinity is 2/3

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Thanks so much for these awesome videos. As a first-year math major, all of this stuff is so new to me (and it can be pretty complex to understand at first), and sadly there are very few places to get help with it. The Math Stack Exchange is great, but having videos like yours are fantastic! It's as if you're sitting here and helping me through the problems step-by-step.

Keep up the great work! I hope you get to 1/2 million subscribers soon! That'll be an awesome milestone. Cheers!

andrewcameron

This solves all my problems with sequence limits. Big thanks to your hard works.

phuongbui

It's so clear that ı will study with these videos

erenturkylmaz

what would you do if the denominator had a minus value in it? such as 31/9(9n-7)? since 31/9(9n-7) > 31/9(9n)

joshseng

I'm doing real analysis this semester, I'm a Mathematics Major by the way. Thanks for sharing this video. It helped a lot. Sadly after doing a lot of Calculus courses, 1 to 4, Real Analysis has not been as intuitive with all the proof writing and the overall thought process that has to be employed. Is it too hard to introduce Real Analysis and even Discrete Mathematics to students at a much earlier stage??? Does it even make sense to do so? I really wish I had the opportunity to see this material much earlier in my Math journey. Again, great video. I subscribed!

Tuffadandem

Whoosh, right over my head prof... glad I'm only interested in calculus, and that only at calc 3 level. But I always look on the bright side...I can make things. Thanks for the video nonetheless...always interesting.

isobar

Hey man! Why this kind of proof doesn't work with other numbers, for instance 3/4 or 1/3? Is it because you wouldn't get a numerator without any ns? For example I did it for 3/4 and i found (17-n) / (12epsilon) < n so I understand it is kind of useles...

samuelmolano

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