Take it easy

Algebra Level 3

for any integer k>1000 \[A= \large \displaystyle\sum_{n=1}^{k}(-1)^{\frac{n(n+1)}{2}}n + \large \displaystyle\sum_{n=1}^{k+1}(-1)^{\frac{n(n+1)}{2}}n + \large \displaystyle\sum_{n=1}^{k+2}(-1)^{\frac{n(n+1)}{2}}n + \large \displaystyle\sum_{n=1}^{k+3}(-1)^{\frac{n(n+1)}{2}}n\] if the sum of all possible values of A is m post your answer as 2m . note: don't combine the repeated values.

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