Recent content by ankitkr

Ok here's a question...n I'm totally lost..maybe a lil push in the right direction or just a start wud really help :) Prove(by induction) that for every n element of N(natural numbers).. there exists a natural number k, such that n <= k^2 <= 2n

hey... how abt you do this for the inductive step now u suppose k^2 <= k! for some k>4 then, k+1 = k(1+1/k) < k^2 , since (1+1/k) <= 2 < k. Thus... (k+1)^2 = (k+1)(k+1) < (k+1)(k^2) <= (k+1)(k!) = (k+1)! therefore... (k+1)^2 < (k+1)! hope this helps...