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#1 Re: Help Me ! » To solve recurrence relations by iterations » 2010-03-29 10:12:03

Hello,

I don't understand, what you want to solve. I assume that you want to find an explicit formula for your reccurence.

Then we have

Now, we can prove this by induction. First step is for k=1. This trivially holds. Assume correctness for k = n.


Now we need to prove the identity

That's easy. Try it.

Izmael

#2 Re: This is Cool » Integral challenge for masters » 2010-03-29 09:45:36

Can't find any benefit on your answer. I know, there exist many same solutions on the internet for this problem. It should be a challenge. So you can bring new inovative approach to solve this.

Your third link is not correct. There's a function sin(ln(x)), which is a bit different.

My approach was about using the exponential

.

#3 This is Cool » Integral challenge for masters » 2010-03-28 09:39:01

Izmael
Replies: 3

Hi,

this integral was introduced as a problem in qualification round for regional olympiad. It took me an hour to solve. Can you solve it too?

I'm looking for your suggestions,
Izmael

#4 Re: Help Me ! » Vec Vec Vector!! » 2010-03-28 09:34:53

Hi,

it will be much easier to take equation

Now, it is possible to multiply by x_j, so we have


Since 2-norm is always positive for nonzero vector x, we have c_j=0 for all j.

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