need help with math1241 questions (1 Viewer)

[brett86]

determine the convergence or divergence of Σa_n for the following a_n:

thanks in adv to anyone that can help

 

[withoutaface]

Well the second one diverges because its terms are all > than those of the harmonic series (1/n) which we know diverges.

 

[Li0n]

waf..
do you really have a girlfriend?
but yeah.. the imaginary one is she really hotter than dreamerish :O:O

 

[MAICHI]

The first one you would argue that (log(n))^3 < (n^(1/9))^3 = n^(1/3) for large n, now since n^(1/3) as the numerator converges so does the series.

The second one you would do a comparison test with 1/n, eg [1/n^(1+1/n)]/[1/n] = 1 as n approaches infinity, and we know that if one series diverges both series diverges, so the original series diverges since 1/n diverges.

The third one is just like the first one I think, log(n!) < n^(3/2) for large n.

 

[gman03]

the third one use the fact that log(n!) < log(nⁿ) = n log n

 

[brett86]

thanks withoutaface, MAICHI, and once again, gman03 for ur help!