for problem 3-7 find each sum or show that it diverges.

ASSIGNMENT #4 MATH 2414 CALCULUS II (1) Suppose you have a ball such that the ratio of how high it bounces to how far it fell is r (r is the "bounciness" of the ball). Find the bounds for r and if the ball is dropped from height a onto a level surface, how far the ball will travel (up and down) before coming to a rest. (2) Let a1 = 5, a2 = 5/3, a3 = 5/9, ... (a) Find a formula for the nth term, an. (b) Find lim an. (c) Find a formula for the nth partial sum, Sn. (d) Find > an n= 1 For problems (3) - (7), find each sum or show that it diverges. (3) nsin(1) n = 1 (4) arctan(n) - arctan(n + 1) n =1 (5) 6) n -3 / 4 (7) 3 1n(n) n\f