mon
Posts:
46
Registered:
12/6/04


Re: Induction proof
Posted:
Aug 20, 2006 7:40 PM


>> I want to understand why >> 1/(n+1)^2 < 1/(n*(n+1))
I am talking about the same thing but more informally. I just wrote "I" instead of "You":)
"Dave L. Renfro" <renfr1dl@cmich.edu> wrote in message news:1156024536.128486.292580@i42g2000cwa.googlegroups.com... > kp wrote (in part): > >> I want to understand why >> 1/(n+1)^2 < 1/(n*(n+1)) > > Statements: > > 1. 0 < 1 > > 2. n < (n+1) > > 3. n(n+1) < (n+1)(n+1) > > 4. 1 / [n(n+1)] > 1 / [(n+1)(n+1)] > > Reasons: > > 1. 1 is a positive number. > > 2. Add n to both sides of #1. > > 3. Multiply both sides of #2 by the positive number n+1. > > 4. Apply the function f(x) = 1/x, which is strictly decreasing > for x > 0, to both sides of #3. Recall that "f is strictly > decresing for x > 0" means "a < b and a,b > 0 ==> f(a) > f(b)" > is true. > > Dave L. Renfro >

