Question

prove that 4^k > k^3

Answer 1

for k integer?

Answer 2

i mean k positive integer?

Answer 3

cantor it would work for non integers to... trying to think how you would prove it though

Answer 4

sorry..should have mentioned the conditions...k are positive integers...need to prove by mathematical induction..

Answer 5

thought so..... I was about to say induction

Answer 6

well when k = 0 the expression becomes 4^0>0^3 which becomes 1>0 which is true and as the value of k increases the first side of the expression increases at a much more rapid rate so that is why this is going to be true for all positive integers of k

Answer 7

check this page out
http://answers.yahoo.com/question/index?qid=20101204110027AASBIgf
it is similar to your problem and should walk you through the process, which is a long process

Answer 8

yes Nikko..that is true. but this is by intuition...proof by induction is bit complicated

Answer 9

give the base case, inductive hypothesis , and then prove by induction

Answer 10

thank you Nadeem...i'll go through the site

Answer 11

the only difference is that they had a parameter where \[n \ge5\]

Answer 12

give me a sec to work this out