Question

Question : 

Let Vr = (Ur+1)^2 - (Ur)^2 = [ (n-2)((2n-3)]/ (n^2 + 1) , where n>= 1 and Ur>0

Show that (1/2)<= Vr <2


My first though was to apply limits, resulting the right side of the equation and then appying Mathematical Induction gave the left hand side of the inequality.

Could you please guide me through a possible method of solving the above simulataneously, or without using principles of Mathematical Induction.
Or what could possibly be the most appropriate method for solving this?.

Thanks!

Answer 1

(Ur+1)^2 - (Ur)^2 = 2Ur + 1
not sure what that has to do with n.

I guess I don't understand what Vr and Ur represent.

Answer 2

Ur+1 , Ur denote r+1th and rth term of a sequence respectively.

Vr = Ur+1 - Ur

Sigma Vr= [(n-2)(2n-3)]/(n^2 + 1)

Ur>0 and n>=1

Answer 3

Let me post the question again