the poster above has the main idea of this problem well in hand, so i have little to add to that solution. however, you will find the following comment helpful:
if you're given the definition of a sequence, with 'a sub k' or similar, then WRITE OUT THE FIRST FEW TERMS OF THE SEQUENCE.
if you do this here, then you'll realize that the sequence is
1 -1 3 -3 5 -5 ...
and the SUMS after each of those terms are added are
1 0 3 0 5 0 ...
if you do this, then the patterns are quite obvious:
terms: the odd-numbered terms are positive and the even-numbered terms are negative
sums: the sums up to odd-numbered terms are positive and odd, while the sums up to even-numbered terms are all zero
the rest follows.
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in general, the more formulaic mumbo-jumbo there is in a problem, the more likely it is that you'll be able to solve the problem just by grinding out the sequence until its patterns become apparent.
Ron has been teaching various standardized tests for 20 years.
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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