Each term seems like it's -3 times the previous one, first term 2.
[tex] \displaystyle \sum_{k=0}^{\infty} 2 (-3)^k [/tex]
Going to infinity like that it's of course divergent, but perfectly summable if we replace infinity with a finite bound like n-1:
[tex] \displaystyle \sum_{k=0}^{n-1} 2 (-3)^k [/tex]
But, assuming the pattern continues means I'd go with infinity.
Answer: [tex] \displaystyle \sum_{k=0}^{\infty} 2 (-3)^k [/tex]
