Remarca
Daca luam in seama valabilitatea conjecturii lui Andrica, i.e. \( \sqrt{p_{n+1}}-\sqrt{p_{n}}<1 \), atunci seria noastra ar fi majorata de seria \( \zeta(2)=\sum_{n\ge 1}\frac{1}{n^{2}}=\frac{\pi^{2}}{6} \), deci ar fi convergenta.
Serie convergenta oare?
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Cezar Lupu
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Serie convergenta oare?
Hmmm gandindu-ma asa la diverse serii si fiind inspirat de acest topic, ma intreb oare daca seria \( \sum_{n \ge 1}\frac{\sqrt{p_{n+1}}-\sqrt{p_{n}}}{n^{2}} \) este convergenta?
Remarca
Daca luam in seama valabilitatea conjecturii lui Andrica, i.e. \( \sqrt{p_{n+1}}-\sqrt{p_{n}}<1 \), atunci seria noastra ar fi majorata de seria \( \zeta(2)=\sum_{n\ge 1}\frac{1}{n^{2}}=\frac{\pi^{2}}{6} \), deci ar fi convergenta.
Remarca
Daca luam in seama valabilitatea conjecturii lui Andrica, i.e. \( \sqrt{p_{n+1}}-\sqrt{p_{n}}<1 \), atunci seria noastra ar fi majorata de seria \( \zeta(2)=\sum_{n\ge 1}\frac{1}{n^{2}}=\frac{\pi^{2}}{6} \), deci ar fi convergenta.
Last edited by Cezar Lupu on Fri Apr 04, 2008 8:55 pm, edited 2 times in total.
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