Melody

Hi guest,

My original answer (the one you referred to) does look at the multiplication of 2  two digit numbers 

The header row is the units digit of the first number 

The header column is the units digit of the second number.

What I did not take into consideration is that the numbers are supposed to be different from one another.

This makes the question much more difficult.  Each cell will no longer occur an equal number of times.

So I have redone it.  I think this method is right but I am less confident than i was with the original answer.

So the probability will be  4/100 = 0.04     (I have fixed a typo)  Thanks guest  

This is a super easy proof.

Hint:    \(Cos(2A)=cos^2A-sin^2A\)

Thanks very much Tiggsy,

Unfortunately you lost me from here:

"Construct a difference table to find "

Why is   

\(\Delta^{2} f_{0}=\Delta^{3}f_{0}=\Delta^{4}f_{0}=0 \)

I thought they would all be 1      

Can you show me the common difference table that they come from?

They are the only ones.

Your answer:

No I do not notice that!

You will need to explain your provided solution.

Do you actually understand it ??

Ginger's way looks fine to me.

You only need to find the value of  f.

To solve this would be extremely time consuming but I do not think it would be that difficult.

If you are prepared to put in an hour or 2 or 3 of time it should be quite solvable.

Start with this Venn diagram.

Put the middle one in first and then work outwards.

Yes that is correct.

Please put your questions in the question space.

The title could have been

"Infinite sum of a series"