Proof by Induction - Inequalities

[odolwa99]

Homework Statement

Prove by induction that: (Please see attachment)

Homework Equations

The Attempt at a Solution

Can someone please confirm if I have worked the question out correctly. Many thanks.

 

[ehild]

Your method is not correct. Start from the inequality you supposed to be true (for n=k) and transform it till you arrive to the desired form. You started from the case n=k+1 and went backwards. That is wrong. ehild

 

[HallsofIvy]

It might help you to note that
$$\frac{1}{(1+r)^n}\le \frac{1}{1+ rn}$$
is exactly the same as
$$1+ rn\le (1+ r)^n$$
so you don't have to worry about the fractions.

 

[boaz]

the second line from the end looks incorrect.
$\frac{1}{k\cdot r^2} \le 0 \Leftrightarrow k<0, r\ne 0$
why won't you try to attack it from another aspect. for example,
$p_1>p2>0 \rightarrow \frac{1}{p_2}>\frac{1}{p_1}$

 

[odolwa99]

Thank you for the help guys. I genuinely appreciate it.