ku1005

04-15-2007, 02:21 AM

Using properties of limits show that thereexists an N in the set of positive integers such that

n>N => ((n+1)^2)/2n^2 < 3/4

For this question, would someone be able to show me a more succinct approach, as I belive the process I used isnt very efficient, say I had to apply it to a different Q which was harder, or maybe Im wrong and the way I solved it is fine???...any suggestions great!!

I simple took the limit of the sequence as it went to infinity, ie divide all by n^2

therfore you obtain (1 + 2/n + 1/n^2) / 2

which as -> inifnity obviously = 1/2 which is less then 3/4

therfore, I SUB each number (this this bit I dont like- i belive ther is usually a way you can solve for this number) and found that once n> 4, then the seq is always less then 3/4

hence N = 4

cheers for any help suggestions as always!!!

n>N => ((n+1)^2)/2n^2 < 3/4

For this question, would someone be able to show me a more succinct approach, as I belive the process I used isnt very efficient, say I had to apply it to a different Q which was harder, or maybe Im wrong and the way I solved it is fine???...any suggestions great!!

I simple took the limit of the sequence as it went to infinity, ie divide all by n^2

therfore you obtain (1 + 2/n + 1/n^2) / 2

which as -> inifnity obviously = 1/2 which is less then 3/4

therfore, I SUB each number (this this bit I dont like- i belive ther is usually a way you can solve for this number) and found that once n> 4, then the seq is always less then 3/4

hence N = 4

cheers for any help suggestions as always!!!