1 Attachment(s)
Re: Valid question or not?
If the attached formula is what you mean, not only that the formula has a bound, it is monotonically decreasing, with a limit at: 2.30277563773199, and highest value at n=1 (a1 = 3).
This can be achieved by assuming there is a finite limit, when approaching the limit, An will be equal to An+1, and therefore:
Code:
An = sqrt(An + 3) ==>
An^2 -An - 3 = 0 ==>
An = (1 +- sqrt(13)) / 2
The minus is not an option because the formula is always positive, so:
Code:
An = (1 + sqrt(13)) / 2 = 2.30277563773199...
But I think that this is not the formula you mean...
Regards,
Zachm
Re: Valid question or not?
How can it be decreasing when the question stated show that its increasing, I sort of understand your way of calculating it but I don't think the formula is right.
Re: Valid question or not?
You can test this, using MS Excel, for instance, I got the following series:
Code:
3.00000000000000
2.44948974278318
2.33441421833898
2.30963508337118
2.30426454283599
2.30309889992505
2.30284582634727
2.30279087768457
2.30277894676944
2.30277635622078
2.30277579373694
2.30277567160523
2.30277564508687
2.30277563932895
2.30277563807874
2.30277563780728
2.30277563774834
2.30277563773554
2.30277563773277
2.30277563773216
2.30277563773203
2.30277563773200
2.30277563773200
2.30277563773200
2.30277563773199
2.30277563773199
2.30277563773199
2.30277563773199
2.30277563773199
I don't know if the question is stated correctly, but if it refers to the formula I attached in my last post, then the series is DECREASING.
Regards,
Zachm