In my view, the video is a little misleading. The proof here only shows that the limit of 0.999 … = 1. But most laypeople interpret the statement as the limit equaling the value. Therefore, the proof should be showing that the geometric series is continuous at 9/10.
An infinite series is convergent if its SOPS is so! Also, the proof is indeed showing that the limiting value of 0.9999999... running up to inf. is equal to 1, that is this infinite sum (0.9+ 0.09+ 0.009+... ) is equal to 1. And sum of an infinite series is nothing but limit of its SOPS. Secondly, a positive term geometric series with modulus of the common ratio less than 1 is absolutely convergent and hence convergent. So nothing to worry here! We hope that it settles your concern. Thanks!
@@TRAILBLAZER-ps3dg Maybe I’m nitpicking … what I meant is that you already showed that 0.9999 … = a but you still need to explain why a = 1. The statement about absolute convergence certainly works
Very interesting 👍😊
Very interesting 👏👏
💯
As always, very well explained ma'am👍👍
Great explanation!!
very nice explanation! 👏
Great explanation!!👏
We know this from very little age but the exact explanation (with multiple proofs) is here.
Glad !
Thank you ma'am 🙂
Clear😊
In my view, the video is a little misleading. The proof here only shows that the limit of 0.999 … = 1. But most laypeople interpret the statement as the limit equaling the value. Therefore, the proof should be showing that the geometric series is continuous at 9/10.
An infinite series is convergent if its SOPS is so!
Also, the proof is indeed showing that the limiting value of 0.9999999... running up to inf. is equal to 1, that is this infinite sum (0.9+ 0.09+ 0.009+... ) is equal to 1. And sum of an infinite series is nothing but limit of its SOPS.
Secondly, a positive term geometric series with modulus of the common ratio less than 1 is absolutely convergent and hence convergent. So nothing to worry here!
We hope that it settles your concern. Thanks!
@@TRAILBLAZER-ps3dg Maybe I’m nitpicking … what I meant is that you already showed that 0.9999 … = a but you still need to explain why a = 1. The statement about absolute convergence certainly works
@@andytam5600 Thanks for your interest!