rasi
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i tried... i can't get tackle with this problem no matter how hard i try. please help me.
could you explain using the "homework template". i'am a little while ago member in this community.HallsofIvy said:All homework posts should use the "homework template" and must show what you have tried yourself on the problem. rasi, if you do not show what you have tried within a couple of days, I will delete this thread.
rasi said:could you explain using the "homework template". i'am a little while ago member in this community.
this is my trial.
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first of all thank for everything...Curious3141 said:First of all, you have to be very careful splitting up infinite series like that (in fact, it doesn't look like you can split it up in this case).
Second of all, the second sum is NOT e. The limit term is e.
This is a tricky sum, and I'm not sure how to proceed either. But I don't think you're on the right track yet, if that helps.
rasi said:i tried... i can't get tackle with this problem no matter how hard i try. please help me.
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Ray Vickson said:For small x > 0 we have x - x^2/2 < \ln(1+x) < x - x^2/2 + x^3/3, so \exp\left(1 - \frac{1}{2n}\right)< \left(1 + \frac{1}{n}\right)^n < \exp\left(1- \frac{1}{2n} + \frac{1}{3n^2}\right).
RGV
rasi said:you right. this book is very difficult. is there any book that you know which is starting elementary? and has much examples with solutions. about sequences, series, limit, differentiable, derivative, integral
Curious3141 said:I didn't check this, but even assuming it's right, does it help to sum the series? Establishing convergence is quite easy, it's the sum that's killing me.
Ray Vickson said:The inequalities above help to bound the terms of the original series between terms of two divergent series, so (assuming I have not made any errors) I get that the series is divergent. I am curious to know how you established convergence.
RGV
When you first click on the "new thread" button in any of the homework forums, you get a "template" with things like "statement of the problem" and "Attempt at a solution". You chose to erase those. Don't do that!rasi said:could you explain using the "homework template". i'am a little while ago member in this community.
this is my trial.
Dick said:What Ray Vickson is trying to show is that difference between e and (1+1/n)^n is greater than a term of the order of 1/n. So the difference will diverge like a harmonic series.