Practice for Math Club

Many member noticed that there is a pattern within the power of *i*.

*I* = sqrt(-1)

*I*² = -1

*I*³ = -sqrt(-1) = –*I*

*I^4* = +1

And they separated i, i³ and i², i^4 and made two equations.

*I*– 3*l*+ 5*I*– 7*I*……+ 1001*I*

If we pair the two numbers starting from the beginning, there are exactly 250 pairs and they all equal -2*I* with extra +1001*I.*

So 250 X (-2*I*) = **-500 I** and adding

**+1001**

**gives**

*I***501**

*I*

2) -2 + 4 -6 + 8……. + 1000

We can simplify this to understand more easily

2(-1 + 2 – 3 + 4 …. + 500)

We notice that there are 250 pairs which result of 1

2(250*1) = **500**

So ∴ 500 + 501*I*

Easier way is

Referenced from

http://cs.smu.ca/~nsml/OldContests/2010Game2Problems.pdf

http://cs.smu.ca/~nsml/OldContests/2010Game2Solutions.pdf