Induction Help (Inequalities) (1 Viewer)

[Sleight_of_Hand]

Hey Guys I was searching through the forums for induction inequalities questions and I realised i dont understand something. Why is it that below (image), after subsituting the n = k formula into the n= k + 1 formula the LHS becomes greaterthan or equal to the new equation formed

 

[Pwnage101]

i.e. adding a non-negative number to any number results in something that is at least as great as the original number. Fairly intuitive.

 

[annabackwards]

Ok. You have LHS = (1+x)^k x (1+x)

Now the assumption says that (1+x)^k >= 1+kx

If you think about it logically, if you multiply both side by an integer (greater than zero) we'll call it B then:

B (1+x)^k >= B(1+kx)

Now if the integer B happens to be (1 + x) then you have

(1+x)^k(1+x) >= (1+kx)(1+x)

That's why the above expression is true.

 

[nikkifc]

This is from a CSSA trial. The second part is more interesting I think.

 

[juppie168]

i.e. adding a non-negative number to any number results in something that is at least as great as the original number. Fairly intuitive.

true true and there is another way to do this question in a more easier way too!