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HGL
science forum beginner

Joined: 11 May 2005
Posts: 4

Posted: Wed May 11, 2005 8:24 am    Post subject: HELP on Infinite Series

Need help on whether the following series converge or diverge:

SUM,n=1,infinity (e/pi)^n-1

SUM,n=1,infinity n^3e^(-n^3)

SUM,n=1,infinity (n^2+1)/(n^3+1)

Thanks
Torsten Hennig
science forum Guru Wannabe

Joined: 28 Apr 2005
Posts: 136

Posted: Wed May 11, 2005 3:26 pm    Post subject: Re: HELP on Infinite Series

 Quote: Need help on whether the following series converge or >diverge: SUM,n=1,infinity (e/pi)^n-1 Hint: e/pi < 0.9 SUM,n=1,infinity n^3e^(-n^3) Hint: e^(-n^3) = 1 / (1+n^3+0.5*n^6+...) < 2/n^6 SUM,n=1,infinity (n^2+1)/(n^3+1) Hint: (n^2+1)/(n^3+1) >= 1/n Thanks

Best wishes
Torsten.

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