A problem for a novice!

Level pending

Answer the following problem:

1-2+3-4+5-6+7-8+9-.......+999


The answer is 500.

Dayra Hernández Rodríguez by Dayra Hernández Rodríguez , 27

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3 solutions

Finn Hulse
Jan 29, 2014

First off I am not a novice, nor is anyone who dedicates their time to challenging themselves with math when they could be playing video games. Second, let's solve the problem. It's obvious that after looking at the results that this equation has a pattern when it is evaluated: 1, -1, 2, -2, 3, -3, etc.. It appears that for the nth term, the number is -1 to the n - 1 power times n over 2, rounded up if n is odd. Plugging in 999, we see that the answer is 500.

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Each 2 numbers is 1, example: 1-2 is -1 and -1+3 is 2 and the sequence is: 1, -1, 2, -2, 3, -3, 4, -4....... Also, you can do a division: 999 number / each 2 numbers is a integer, and the answer is 499 with 1. So, 499+1=500. The answer is 500.

Sorry if my english isn't perfect, i speak spanish.

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Akriti Kalra
Jan 29, 2014

Split into 2 arithmetic series S(odd terms) = 1+3+5+...+999 (total 500 terms) S(even terms) = 2+4+6 ... + 998 (499 terms)

S= s(odd)-s(even) = 250(1000)-249.5(1000) = 500

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