For each of the series below select the letter from a to c that best applies and the letter from d to j that best applies. A possible correct answer is af, for example.

A. The series is absolutely convergent.
B. The series converges, but not absolutely.
C. The series diverges.
D. The alternating series test shows the series converges.
E. The series is a p-series.
F. The series is a geometric series.
G. We can decide whether this series converges by comparison with a p series.
H. We can decide whether this series converges by comparison with a geometric series.
I. Partial sums of the series telescope.
J. The terms of the series do not have limit zero.

1. $\displaystyle \sum^\infty_{n=1} (-1)^n \; \int^{n+1}_n {7 } ^{-x} dx$
2. $\displaystyle \sum^\infty_{n=1} \; \frac n{n+7 ^n}$
3. $\displaystyle \sum^\infty_{n=1} \; \frac{n^{3 }}{3 ^n}$
4. $\displaystyle \sum^\infty_{n=1} \left( 1 + \frac{3 }{n} \right)^n$
5. $\displaystyle \sum^\infty_{n=5} \; \frac{ (6 -1) \cdot ((2) 6 - 1) \cdot \cdot ((n - 1)6 - 1)} {6 ^n (n!)\sqrt n}$
6. $\displaystyle \sum^\infty_{n=1} (\log (n+1) - \log n)$

You can earn partial credit on this problem.