[www.keralites.net] HELP PLEASE!!!!!

Guys,  i need your help...kindly solve this mathematical problem for me. I'm not good in math. Please read and analyze the problem carefully and send me your answers  as soon as possible, ok? 

Legend has it that while in grade school, one of the greatest mathematicians, Carl Friedrich Gauss was able to add the numbers 1 to 100 mentally, Gauss did not add them sequentially, but rather paired 1 with 99, 2 with 98, 3 with 97, and so on.

1.Use a method similar to gauss's to simplify the following:

   1+2+3+4+5+6+7+8+9+10.

2.How were the associative and commutative laws applied in question 1?

3.Use Gauss's method to find the sum of the first  100 counting numbers:

   1+2+3...+48+49+50+51+...+97+98+99+100.

   ~How many pairs of numbers that add up to 100 are there? Is there any number left?
   ~What is the total sum?

4.Find the sum of the first 200 counting numbers. What are the number pairs?

   How many pairs will there be?

 Thanks a lot,
Elsie Naval

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www.keralites.net

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