1996 AJHSME Problems/Problem 16
Contents
[hide]Problem
Solution
Put the numbers in groups of :
The first group has a sum of .
The second group increases the two positive numbers on the end by , and decreases the two negative numbers in the middle by . Thus, the second group also has a sum of .
Continuing the pattern, every group has a sum of , and thus the entire sum is , giving an answer of .
Solution 2
Let any term of the series be . Realize that at every , the sum of the series is 0. For we know so the solution is .
~Golden_Phi
See Also
1996 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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