query: Why can infinite series be summed different ways to get different results?
positive_passages.docid: 155593
positive_passages.text: absolutely convergent series and conditionally convergent series rearrangement
negative_passages.docid: 27224
negative_passages.text: Infinite series $\sum_{k=1}^\infty \frac{k}{2^k}$ and $\sum_{k=1}^\infty \frac{k^2}{2^k}$
negative_passages.docid: 17214
negative_passages.text: Transfinite series: Uncountable sums
negative_passages.docid: 157001
negative_passages.text: Are there clever ways to evaluate this infinite series?
negative_passages.docid: 132351
negative_passages.text: Is the infinite sum of $2 ^{-n}$ convergent? Why?
negative_passages.docid: 25504
negative_passages.text: How to find sum of the infinite series $\sum_{n=1}^{\infty} \frac{1}{ n(2n+1)}$
negative_passages.docid: 110585
negative_passages.text: Rearranging infinite series
negative_passages.docid: 146587
negative_passages.text: Why does the series $\sum_{n=1}^∞ \ln ({n \over n+1})$ diverges? And general tips about series and the logarithm
negative_passages.docid: 143828
negative_passages.text: Why does an conditionally convergent infinite series, when deranged, have a different limit?
negative_passages.docid: 1560
negative_passages.text: Shouldn't the harmonic series converge?
negative_passages.docid: 150459
negative_passages.text: Suppose $\sum\limits_{n=1}^\infty b_n$ diverges and $b_n\gt 0$, show that the series $\sum\limits_{n=1}^\infty \frac{b_n}{1+b_n}$ also diverges
negative_passages.docid: 59485
negative_passages.text: Infinite Series: $\sum_{n=1}^\infty \frac{1}{2^nn}$
negative_passages.docid: 125981
negative_passages.text: Closed-Form Solution to Infinite Sum
negative_passages.docid: 56231
negative_passages.text: Infinite series for $e$...
negative_passages.docid: 77201
negative_passages.text: Convergent or divergent series ? Given that $\sum a_n $ is already convergent.
negative_passages.docid: 55061
negative_passages.text: Evaluating the sum after reordering an infinite series $1-\frac {1} {2}+\frac {1} {3}-\frac {1} {4}+\ldots $
negative_passages.docid: 115816
negative_passages.text: Grandi's Series; tends to $1/2$, but why is this considered a valid sum?