Question

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

Answer 1

ratio test should do it

Answer 2

oh and the answer is yes, it converges

Answer 3

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

Answer 4

yeah me too

Answer 5

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

Answer 6

ohhhh ok! got it thanks again!!!

Answer 7

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

Answer 8

yw again

Answer 9

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

Answer 10

haha I will let you know if i get it!