1. Let (a n ) be a sequence of nonnegative real numbers. Prove that a n converges iff the sequence of partial sums is bounded 2. Let (x n ) be a sequence of real numbers and let y n = x n – x n+1 for...

1. Let (a_n) be a sequence of nonnegative real numbers. Prove that
a_n
converges iff the sequence of partial sums is bounded

2. Let (x_n) be a sequence of real numbers and let y_n
= x_n
– x_n+1
for each n.

(a) Prove that the series
 converges iff the sequence (xn) converges.

(b) If
 converges, what is the sum?