Posted by Dina on Friday, September 21, 2007 at 2:00pm.
If 2^n>n^2 and n>5, then 2^n+1>(n+1)^2
Proof: Assuming that 2^n>n^2 then I can say that 2*2^2>2*n^2 = 2^n+1>2n^2
If I can show that 2n^2>(n+1)^2 then I will be done by transitivity. So 2n^2>(n+1)^2? then 2n^2>n^2+2n+1? then n^2>2n+1, hence n^22n1>0, and if I add 2 then n^22n+1>2... after this I do not know what to do. If you can see that I did something wrong somewhere along the proof please let me know.

Abstract Algebra  bobpursley, Friday, September 21, 2007 at 2:34pm
Proof: Assuming that 2^n>n^2 then I can say that 2*2^n>2*n^2 = 2^n+1>2n^2
yes, correct
If I can show that 2n^2>(n+1)^2 then I will be done by transitivity.
So 2n^2>(n+1)^2?
then 2n^2>n^2+2n+1?
then n^2>2n+1, now, n>5, so n= 5+m, where m is any positive integer.
n^2 >2n+1
(5+m)^2>2(5+m)+1
25+2m + m^2>10+2m+1
m^2>14, and since m is any postive integer, it is proved.
Answer This Question
Related Questions
 Math (Proof)  Prove that if ab = ac (mod n) and a is relatively prime to n, ...
 CHEM ABSTRACT  I need to write an abstract for my chemistry lab for identifying...
 informal Logic  God must exist for there can be no other explanation for the ...
 abstract algebra  Let R be a ring. The center of R is the set C= {x exists in R...
 Algebra II  In an induction proof of the statement 4+7+10+...+(3n1)=n(3n+5)/2 ...
 Logic Formal Proof  I need to solve a proof and I cannot figure it out. The ...
 Abstract Algebra  Let A= {1}, that is, the set of all real numbers except 1...
 Algebra  Write a direct algebraic proof to show that if a/b=c/d, then a+c=b+d
 Math  Please help me with this problem: A bourbon that is 51 proof is 25.5% ...
 Algebra  can show me how to do this with out just squaring 3x^(1/2)  x  6 = 0...
More Related Questions