N1=2, N2=3, N3=5, N4=6 , ... , Ni=i-th non square integer.Please help me with a solution to the following problem,I've been trying this for somedays but is unable to approach it in any way...
It is found that for some integer m, m^2< Nn <(m+1)^2
Prove that m= [√n + (1/2)] where [x]=Greatest Integer Function.
Thanks a lot guys...I've solved it in another way 2...
Nn=n+1 , 1<= n <=2
=n+2 , 3<= n <=6
=n+3 , 7<= n <=12...
=n+k , k^2 - k + 1 <= n <= k^2 + k
From here a little simplification tells that "(√n + 1/2)-1 < m < √n + (1/2)"
which clearly implies the proof...