I need help with inductive reasoning The sum of the first 1,000 counting numbers are ? Help?

Question

I need help with inductive reasoning The sum of the first 1,000 counting numbers are ? Help?

Answer 1

Well, I know that the  sum of the number of odd numbers equal the squares of the number of numbers, example is , the first 4 odd numbers are 1 3 5 and 7, you add them and get 16 , which when you square root you get 4, so if there are 500 odd numbers in 1000, it would be 500^2For the Even numbers i know that it is the number of numbers times the number of numbers plus one, example is, the first 4 even numbers are 2 4 6 and 8, when you add them you get 20, which is 4x5

So, if you do 500^2 (250000) + 500x501 (250500) you get 500500 :P

Hope that helped, I dont know if there is an easier way...  

Answer 2

500500

http://mathcentral.uregina.ca/QQ/databas...

that site explains the reasoning and gives a formula.

Answer 3

Take the first and last and add them ...

1 + 1000 = 1,001

Now the second and 2nd from last ...

2 + 999 = 1,001

Now if you continue that you'll notice your answer is always 1,001 since one number goes up one and one goes down one.  You'll do that 500 times. So your sum would be ...

500 x 1,001 = 500,500

Answer 4

1 + 1000 = 1001

2 +  999 = 1001

3 + 998 = 1001

...

500 + 501 = 1001

So we have 500 pairs of numbers that sum to 1001. That means the sum of 1 + 2 + 3 + ... + 1000 = 500 * 1001 = 500500.

Answer 5

think about it, 1 + 2 +  .... 1000 is the same as 1000 + 999 + ....1 , therefore if we put these two answers together, (1 + 2 + ...1000) + (1000 + 999 ... + 1) we will get 2 times the sum. But the first term of our equation + the first term of the second = 1001, and so does every other term, (1 + 1000) = 1001,( 2 + 999) = 1001 etc. therefore we get twice the sum = 1001 times the number of terms, or 2s = 1001 * 1000 so the sum =

s = (1001* 1000)/2