1. ## inequality

Hi everyone,
Can you help me to prove that
(1-b^(m+1))(-(b+1))/b^2<(1+b+b^2+b^3+...+b^m)
in logestic way

If you can try to answer me today because I have exam tomorrow in it

Thanks for any helping

2. Originally Posted by rosana
Hi everyone,
Can you help me to prove that
(1-b^(m+1))(-(b+1))/b^2<(1+b+b^2+b^3+...+b^m)
in logestic way

If you can try to answer me today because I have exam tomorrow in it

Thanks for any helping
i'd probably try induction. did you learn mathemtical induction?

3. Originally Posted by rosana
Hi everyone,
Can you help me to prove that
(1-b^(m+1))(-(b+1))/b^2<(1+b+b^2+b^3+...+b^m)
in logestic way

If you can try to answer me today because I have exam tomorrow in it

Thanks for any helping
Do you mean, for $\displaystyle b\not =0$:
$\displaystyle \frac{(1-b^{m+1})(-(b+1))}{b^2} < 1+b+b^2+...b^m$
Note that if $\displaystyle b=1$ then it is trivial.
Assume that $\displaystyle b\not = 1$ then:
$\displaystyle \frac{(1-b^{m+1})(-(b+1))}{b^2} < \frac{1-b^{m+1}}{1-b}$
If $\displaystyle |b|<1$ then $\displaystyle 1-b^{m+1}>0$ and hence:
$\displaystyle \frac{-(b+1)}{b^2} < \frac{1}{1-b}$
Which is true because LHS is negative and RHS is positive.
If $\displaystyle |b|>1$ then $\displaystyle 1-b^{m+1}<0$ and hence*:
$\displaystyle \frac{-(b+1)}{b^2} > \frac{1}{1-b}$
Thus,
$\displaystyle (b+1)(b-1) < b^2$
Thus,
$\displaystyle b^2 - 1 < b^2$
Which is true.

*)It also depends when $\displaystyle m$ is even or odd, but those a minor details.

4. ## analysis

it need analysis from us
we know that (1+b+b^2+b^3+...+b^m)=(1-b^(m+1))/(1-b)
but how to use it

5. Originally Posted by rosana
it need analysis from us
we know that (1+b+b^2+b^3+...+b^m)=(1-b^(m+1))/(1-b)
but how to use it

This is the Geometric Sum.

6. ## thanks

thaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaanks so much Perfect Hackers

I believe that you can answer any thing because you are genios and fantastic guy

thanks again you help me and now I can get full mark in final exam in mathematical analysis

7. Originally Posted by rosana
you are genios
I know
and fantastic guy
I am the greatest. The world shall bow before my will.

8. Originally Posted by ThePerfectHacker
The world shall bow before my will.
Wow. My will merely states that I'm of sound mind and body. (Hard to believe, I know!) Can you send me a copy of your will so I can see how you do that?

-Dan