query: Is the argument used by the Numberphile video to show that $1 + 2 + 3 + 4 + \dots = -1/12$ valid?
positive_passages.docid: 56169
positive_passages.text: What mistakes, if any, were made in Numberphile's proof that $1+2+3+\cdots=-1/12$?
negative_passages.docid: 121052
negative_passages.text: Where is the mistake? $-1=(-1)^{2/2}=\left(\left (-1\right)\displaystyle ^2\right)^{1/2}=1^{1/2}=\sqrt 1=1$
negative_passages.docid: 74122
negative_passages.text: $ 2.28319 = 0 $ !? - How do I spot the mistake?
negative_passages.docid: 21746
negative_passages.text: How do I show that the sum $(a+\frac12)^n+(b+\frac12)^n$ is an integer for only finitely many $n$?
negative_passages.docid: 152698
negative_passages.text: Evaluation of $\sum_{n=0}^{\infty}\frac{1}{(n^4+n^2+1)n!}$
negative_passages.docid: 114074
negative_passages.text: Intuitive/Visual proof that $(1+2+\cdots+n)^2=1^3+2^3+\cdots+n^3$
negative_passages.docid: 120301
negative_passages.text: How to prove $(-3) \times (-4) = 12$?
negative_passages.docid: 80004
negative_passages.text: Why is $1/i$ equal to $-i$?
negative_passages.docid: 147528
negative_passages.text: Where's the error in this $2=1$ fake proof?
negative_passages.docid: 33705
negative_passages.text: Is $0$ a natural number?
negative_passages.docid: 28912
negative_passages.text: Does this series diverge: $(\sqrt 2-\sqrt 1)+(\sqrt 3-\sqrt 2)+(\sqrt 4-\sqrt 3)+(\sqrt 5-\sqrt 4)+\dots$?
negative_passages.docid: 2932
negative_passages.text: How do I prove this sum is not an integer
negative_passages.docid: 73688
negative_passages.text: Can I use Gödel numbers to make a proof?
negative_passages.docid: 33184
negative_passages.text: Something strange about $\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ and its friends
negative_passages.docid: 107390
negative_passages.text: Why is (-1)(-1) = 1?
negative_passages.docid: 108021
negative_passages.text: What does the factorial of a negative number signify?
negative_passages.docid: 37484
negative_passages.text: Is there an elementary argument to show that $\prod_{n=0}^\infty \frac{2n+1}{2n+3}=0$