Online Problem Solving

Hey Guys Send in your solutions to the following questions:

Rules:
1. It should be your attempt.
2. Try to explain each possible step you thought of.
3. DO NOT use any sort of calculators e.g. Mathematica, Matlab etc.

Questions

Q1) What Are Convergent And Divergent Series? Whats is this series called 1-1+1-1+1-1......?

Q2) Given an orange and a knife. You are allowed to cut the orange 4 times only. Disregarding the size, what maximum number of the orange pieces can you get with these 4 cuts?

Q3) Solve the following differential equation:
(class X and lower stds. are not expected to solve this, but if they do, its very good)

* We should receive your solutions within 10 days from the date of posting, ie. by 18th Nov. 2005.
* Send your solutions at techknowmath@gmail.com. (confirm it with the email address given at the bottom of the page)
* 6 points will be awarded for correct and logical attempt, and results will be posted along with the new set of questions every fortnight.
* We'll try our best and post 3 questions every fortnight. If it gets late please do not mind.

^-^ ***Thank You*** ^-^