Real Analysis I posted this question earlier and got a response . I have further questions on the response. I am including the URL of the previous response: https://www.bartleby.com/questions-and-answers/real-analysis-does-the-series-log11n-from-n1-to-infinity-converge-or-diverge-prove-the-convergence-o/97a36976-4bf8-4a81-bf97-1b9c2d442972 My original question was: Prove that the series Sum of log(1+1/n) from n=1 to infinity converges or diverges. The questions I have on the response are as follows: 1. Why can I just change from log to ln? I seem to recall something about ln and log being interchangeable despite that log is log base 10 and ln is log base e. 2. Why does the sequence of partial sums become (ln(2)-ln(1))+(ln(3)-ln(2))+(ln(n)-ln(n-1))+(ln(n+1)-ln(n))=ln(n+1). I need a lot more detail. I seem to be incredibly dense with Real Analysis, despite earning top grades in my previous classes. There are always parts of the proofs that I do not understand which prevents me from understanding the material. Thank you.
I posted this question earlier and got a response . I have further questions on the response. I am including the URL of the previous response:
https://www.bartleby.com/questions-and-answers/real-analysis-does-the-series-log11n-from-n1-to-infinity-converge-or-diverge-prove-the-convergence-o/97a36976-4bf8-4a81-bf97-1b9c2d442972
My original question was:
Prove that the series Sum of log(1+1/n) from n=1 to infinity converges or diverges.
The questions I have on the response are as follows:
1. Why can I just change from log to ln? I seem to recall something about ln and log being interchangeable despite that log is log base 10 and ln is log base e.
2. Why does the sequence of partial sums become (ln(2)-ln(1))+(ln(3)-ln(2))+(ln(n)-ln(n-1))+(ln(n+1)-ln(n))=ln(n+1).
I need a lot more detail. I seem to be incredibly dense with Real Analysis, despite earning top grades in my previous classes. There are always parts of the proofs that I do not understand which prevents me from understanding the material. Thank you.
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