1. Suppose {an} and {bn} are positive sequences and that there exists N so that n >N = an < bn. Show that if£ bn converges, then so does an.

Suppose that the sequence x0, x₁, x2... is defined by x0 = 0, x₁ = 7, and xk+2 = xk for k≥0. Find a general formula for xk. Be sure to include parentheses where necessary, e.g. to distinguish 1/(2k) from 1/2k. xk = 0

Give an example in which {an} ∞ n=1 and {bn} ∞ n=1 do not converge but {an + bn} ∞ n=1 converges.