From Singapore Mathematic Olimpiade

Two problems:

Find the value of :

(1+3+5+7+9+11+...+99)

------------------------

(2+4+6+8+10+...+100)

and

Suppose that x and y are real numbers that satisfy all the following three conditions: 

3x - 2y = 4 - p 

4x - 3y = 2 + p

x > y

What are the possible values of p ?

Matematika

Post isinya + caranya di comment boxnya ya^^

Simple...

Banyaknya angka nol dari 625! adalah ...

dan...

Terdapat sebuah segitiga dengan panjang sisi-sisinya 9, 12 dan X.

Berapa panjang X maksimal ? X adalah bilangan bulat.

Organic Reactions

What happen if we react Butene with Hydrogen?

What happen if we react Isopropanol with an Acetic Acid?

How do you turn Benzene into Bromobenzene?

Write the complete reaction (step by step).

Post your answer in the comment box

enjoy...

Mathematics problems

These are simple questions:

Prove that for x is an integer:

[ (1/5) X^5 + (1/3) X^3 + (7/15) X  ] is also an integer.

and

1^2 - 2^2 + 3^2 - 4^2 + 5^2 - 6^2 + ... - 2000^2 + 2001^2 = ...

You can answer it in the comment box...

thank you.