Helping students gain understanding and self-confidence in algebra.
japiga wrote:Find the least natural number n, so that anyone bellow divisions may not be shorten:
7/(n+9), 8/(n+10),9/(n+11),…. 31/(n+33)
I found that such number n = 17, but how to prove it?
stapel_eliz wrote:japiga wrote:Yes, sorry. "shorten" means "divided not to be further divided". Or generally, not to be divided at all. Is it now more clear?
japiga wrote:Yes, I am wrong, sorry. Thanks Martingale you are correct, but What is solution? What is the least number for n, such as that each division is not to be further divided for all line: 7/(n+9), 8/(n+10),9/(n+11),…. 31/(n+33) ?
And, to add, solution for "n" should be any integer number, but we are looking for the least one ("the smallest one").
japiga wrote:Thanks! It make sense if final result is 1/2, but I am little confused with original assignment: 7/(n+9), 8/(n+10),9/(n+11),…. 31/(n+33). Why he have line only with those numbers, not for all, like 32/(n + 34), 33/(n+35).... It seems that this rule is valid for any k/(n+k+2). Do you think so?