Using the Monotone Convergence Theorem! | Real Analysis

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Let's see an awesome example of the monotone convergence theorem in action! We'll look at a sequence that seems to converge, as its terms change by smaller and smaller amounts, but it isn't clear what it converges to. Since we don't have a clue how we might express its limit, we cannot use our typical method of just proving it converges using the definition of the limit of a sequence. Instead, we'll prove it is monotone increasing and bounded, and thus converges by the monotone convergence theorem! This example is taken from Real Analysis by Jay Cummings. Highly recommended textbook!

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Please consider sharing this video if you liked it, or make a small donation or monthly pledge to help me continue making the best math content I can, links in description.

WrathofMath
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hello sir, can you give me one example of monotone convergence theorem in daily life?
For my project...

granceluvita
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But the theorem says: if Xn is increasing and bounded above, then it converges to a finite limit. In your example, an is increasing and bounded below……

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