Is the sequence: $\underbrace{2,2,...2}_{1000\text{times}}$ a harmonic sequence? First of all let me give a bit introduction about what is a harmonic sequence. For e.g.: We can say that $1,\frac{1}{2},\frac{1}{3},...\frac{1}{n}$ is a harmonic sequence because if we take the reciprocal of each ter...
I recently encountered this question on MSO, where a user asks about why certain tags appear in the tag overview page. This issue is caused by a synonym that redirects users to a non-existent tag. I've created this SEDE query, and on Stack Overflow alone, a total of 60 approved synonyms exist t...
I recently encountered this question on MSO, where a user asks about why certain tags appear in the tag overview page. This issue is caused by a synonym that redirects users to a non-existent tag. I've created this SEDE query, and on Stack Overflow alone, a total of 60 approved synonyms exist tha...
Typically, the tags with no questions are automatically removed by a script which runs once a day, this process is called tag pruning. However, there is a known bug which causes that if both tags in a tag synonym have zero question, they cannot be removed by this script. See this bug-report: Auto...
How to solve the equation: $(2x)^{x}=14+x^{x}$ ? I am trying to solve this equation in this way: $(2x)^{x}=14+x^{x}\implies 2^{x}x^{x}=14+x^{x}\implies x^{x}(2^{x}-1)=14\implies x^{x}=\frac{14}{2^{x}-1}\implies x\ln(x)=\ln(\frac{14}{2^{x}-1})\implies W(x\ln(x))=W(\ln(\frac{14}{2^{x}-1}))$. Now he...
How to solve the equation: $(2x)^{x}=14+x^{x}$ ? I am trying to solve this equation in this way: $(2x)^{x}=14+x^{x}\implies 2^{x}x^{x}=14+x^{x}\implies x^{x}(2^{x}-1)=14\implies x^{x}=\frac{14}{2^{x}-1}\implies x\ln(x)=\ln(\frac{14}{2^{x}-1})\implies W(x\ln(x))=W(\ln(\frac{14}{2^{x}-1}))$. Now he...
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