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OpenStudy (anonymous):

determine whether the folioing series converges or not: (1/2) + 8 + (243/8) + 64 +...+ (k^5)/(2^k)

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OpenStudy (anonymous):

ratio test should do it

OpenStudy (anonymous):

oh and the answer is yes, it converges

OpenStudy (anonymous):

ok when i do the ratio test i get \[(k ^{5}+1)\div 2K ^{5}\]

OpenStudy (anonymous):

yeah me too

OpenStudy (anonymous):

take the limit as k goes to infinity and you get 1/2 which is less than one, so you win

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OpenStudy (anonymous):

ohhhh ok! got it thanks again!!!

OpenStudy (anonymous):

clear yes? numerator is a poly of degree 5, denominator is a poly of degree 5, ratio of leading coefficients is 1/2

OpenStudy (anonymous):

yw again

OpenStudy (anonymous):

i would love to know how to do your last question though...

OpenStudy (anonymous):

haha I will let you know if i get it!

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