SOLUTION: What is the sum of the arithmetic series below? -100+-95+-90+-85+...+-5+0+5+...+85+90+95+100

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Question 1157063: What is the sum of the arithmetic series below?
-100+-95+-90+-85+...+-5+0+5+...+85+90+95+100
Found 4 solutions by greenestamps, ikleyn, MathLover1, my_user_id:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

Isn't it obvious?

All the terms cancel; the sum is 0.

-100+100 = 0
-95+95 = 0
...
-5+5 = -
0 = 0
---------
-100-95-...-5+0+5+...+95+100 = 0

Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.

ZERO.

Find all the similar opposite terms, that cancel each other.

Ha-ha-ha.             //   It is WELL-KNOWN joke problem . . .

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Do not calculate any sums; otherwise, people will laugh on you.

Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
the sum of the arithmetic series below?
-100+-95+-90+-85+...+-5+0+5+...+85+90+95+100 is
all negative:

all positive

=>

Answer by my_user_id(3)   (Show Source):
You can put this solution on YOUR website!
You can use the arithmetic general term formula to din how many terms are in this series, and then use the sum formula, but if you look closer at the problem, you can see that the terms cancel each other out, so the final sum is 0.