1. For each of the sequences {a, }, find and simplify a formula for { s, }, the sequence of partial sums of {an}. (a) an = 2 ( b ) an = In( 2+ 1) 3 72\f3. Determine if the series _ n sin (1) converges or diverges. Justify your answer. 4. Determine if the series _(x - e)" converges or diverges. Justify your answer.5. Determine if the series E- 1 Vn+ 1 + un converges or diverges. Justify your answer. 6. A rubber ball is dropped from a height of 10 meters and then is allowed to bounce up and down indefinitely. Each time the ball hits the ground it bounces up to a height 80% of that from which it fell. Find the total vertical distance the ball travels before coming to rest