Thread: 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

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?

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 :

Note that if then it is trivial.
Assume that then:

If then and hence:

Which is true because LHS is negative and RHS is positive.
If then and hence*:

Thus,

Thus,

Which is true.


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

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

think for me please

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

think for me please

This is the Geometric Sum.

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

Originally Posted by rosana

you are genios

I know

and fantastic guy

I am the greatest. The world shall bow before my will.

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