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UnkleRhaukusBest ResponseYou've already chosen the best response.0
\[=\sum\limits_{n=4}^{25}\frac{1}{n^2+1}\]
 one year ago

tanjungBest ResponseYou've already chosen the best response.0
i think, the problem wants a rational number
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
hmm http://www.wolframalpha.com/input/?i=sum+%281%2F%7Bn%5E2%2B1%7D%29+from+n%3D4+to+25 well it is rational, , ,
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
if we have interpreted the question correctly, and the wolfram result is the one you are aiming towards, then this wont be a nice problem ,
 one year ago

tanjungBest ResponseYou've already chosen the best response.0
hmmm... is there a method to calculating series of : 1/(n^2+1) + 1/((n+1)^2+1) + ... + 1/((n+k)^2+1) , @UnkleRhaukus ?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
what is the context that the problem came from ?
 one year ago

tanjungBest ResponseYou've already chosen the best response.0
this is a question from one of group math also, in my fb. the question ask to calculate or simplify it
 one year ago

wioBest ResponseYou've already chosen the best response.0
The real question is if there is a simplification of: \[ \sum \frac{1}{n^2+1} \]
 one year ago

wioBest ResponseYou've already chosen the best response.0
Like, maybe partial fraction decomposition could help us?
 one year ago

wioBest ResponseYou've already chosen the best response.0
I'm not familiar with this series actually. I'm not sure how to find it's partial sum.
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
@calculusfunctions that power series u use is for when \(x<1\)
 one year ago

StiwanBest ResponseYou've already chosen the best response.0
@calculusfunctions @mukushla On the topic of the power series, there is this equation: \[\sum_{k=0}^{n}x^k = \frac{1x^{n+1}}{1x}\] If we suppose x < 1 and let n go to infinity, x^(n+1) converges to 0, so the power equation equation becomes \[\sum_{k=0}^{\infty} x^k = \frac{1}{1x}\] So you can use the power series only to calculate infinite series if x<1, but as the sum is finite in this example we could use it as well, if we would be able find a constant factor x so that \[\frac{1}{n²+1} * x =\frac{1}{(n+1)²+1} \forall n \in [4,24] \subseteq \mathbb{N}\] You see immediately that this factor x exists but it is not CONSTANT (it depends on n), so we can't use the power series here. @tanjung I'm pretty sure that the answer UncleRauhkus gave you is the correct one, because I can't see the point of an exercise that would require you to do any calculations beside that, because it certainly would not "simplify" the matter.
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
i meant that power series will not be useful for this problem and there is no way to simplify that expression...if im not wrong
 one year ago

calculusfunctionsBest ResponseYou've already chosen the best response.0
Yes @mukushla and @sitwan you're both right. I know that, that's why I didn't proceed further. I was just thinking out loud.
 one year ago
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