Math Is Fun Forum

I thought that you can help me with this. I've seen this in some textbook and I don't know how do thay measured the product of equation ;

Solve for x ;
10^n+10^n-1+10^n-2+...+10^1+1 congruent to 0 (mod 59)

Is there any way to find out the length of recurrence in a division without actually dividing?
Like: 1/3= zero point 3 recurring -->( how to calculate that there's one digit recurring)

I searched a lot about it but I haven't found a thing! I were assuming that you guys can help me. The question is just what I wrote in title ((Represent sqrt{2}+sqrt{3} on a number line)).what that make this diffrent is that it's not like adding an rational to irrational because there you had a certain start point and you draw a triangle and it would be done but in the problem that I mentioned when you draw first triangle you will have a point that doesn't exist((it's value is not accurate))! And therefore it's stupidness to draw another triangle from that point.Then, what to do?

You have 3 children in a family . What is the probability of having 2 girls ?
I've confuesd . I've tryed this method but I don't know why it is not working!
First for n(s) we can say 2*2*2 (every child have two possibility)so it equals 8 then for n(a) we can say because we want 2 girls so 2 children would have just one possibility namely , 1*1*2 then it would equal to 2. But if you write down every possibilty it would be 3! My approach is the same thing for calculating sub sets of some (X) set that is n(s), and for n(A) as I've mentioned . So if ANYONE knows what's wrong or know a better way than write down all possibilties you can make me delighted by leaving it in the comment! THANK YOU;-)

Why something with negative exponent or a variable at denominator is not allowed to be called polynomial?(I know the rules of polynomial but I don't know why )