=Maths Competition= (do not reply in this thread)

Answer as many questions as possible. 1 mark for correct numerical answer and 1 mark for satisfactory explanation as to how you got that answer. 1 extra mark for easy of writing - use brackets, and set work out neatly! Thankyou.

+++easy+++

1. Find the sum and product of all the terms in the sequence: 1, 1/2, 1/4, 1/8 ...
2. Given that: a = 3^243; b = 27^81, what is the value of (a^2)/(b^2) ?
3. Find the nth term of the sequence: 1, 1/2, 1/6, 1/24, 1/120
4. 12!/n! = 11880. What is the value of n?

---meduim---

5. What is the value of: (1/4) + (1/4)^2 + (1/4)^3 + (1/4)^4 ... ?
6. With how many zeroes does the number 3003! end?
7. What is the sum of the digits of (2^202)(5^204)?
8. Find x, if: 9^(2x) = 2*9^x + 3

===hard===

9. Convert 1847 (base 9) into base 4
10. If y/(x-z) = (x+y)/z = x/y, when x, y and z are distinct positive integers, then what is the ratio of x to y?
11. Find the area of the largest equilateral triangle that can be inscribed in a rectangle with sides 10 and 11.
12. Find the largest value of k, such that 3^(11) is the sum of k consecutive positive integers.

PM all results to me, giving the numbers for each (eg. "2. 1304 - because ..."). Any questions, please ask in the other thread:

http://www.uk-learning.net/t54634.html

Good luck everyone!

Remember, NO ANSWERS IN THIS OR THE OTHER THREAD PLEASE.
Thankyou.