How prove this series $\sum_{n=1}^{\infty}\frac{1}{n^3(\sin{n})^2}$ convergent?

Asked Nov 02 '13 at 04:19

Active Nov 02 '13 at 04:26

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prove or disprove this series $$\sum_{n=1}^{\infty}\dfrac{1}{n^3(\sin{n})^2}$$ convergence?

My idea: note

$$|\sin{n}|\le 1$$ so $$\dfrac{1}{n^3(\sin{n})^2}\ge\dfrac{1}{n^3}$$ then this idea is not usefull

other idea

maybe use

$$|\pi-\dfrac{m}{n}|<\dfrac{1}{n^{41}}?$$ But I can't,Thank you

asked Nov 02 '13 at 04:19

5

This question is hard. For more details, see http://mathoverflow.net/questions/24579/convergence-of-sumn3-sin2n-1 – Euler....IS_ALIVE Nov 02 '13 at 04:39
This question isn't actually off-topic, but it has received a full answer at MO. – davidlowryduda Dec 11 '13 at 18:21

0 Answers0