Tính tổng S trong mỗi trường hợp sau :
\(\eqalign{ & a)\;S = 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 \cr & b)\;S = 1 - 2 + 3 - 4 + 5 - 6 + ... + 2013 - 2014. \cr} \)
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\(\eqalign{ & a)\;S = 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 \cr & = ( - 2 + 1) + ( - 4 + 3) + ( - 6 + 5) + ( - 8 + 7) + ( - 10 + 9) \cr & = ( - 1) + ( - 1) + ( - 1) + ( - 1) + ( - 1) = - 5 \cr & b)\;S = 1 - 2 + 3 - 4 + 5 - 6 + ... + 2013 - 2014 \cr & = (1 - 2) + (3 - 4) + (5 - 6) + ... + (2013 - 2014) \cr & = \underbrace {( - 1) + ( - 1) + ( - 1) + ... + ( - 1)}_\text{1007 số hạng} = - 1007 \cr} \)