Mathematical Analysis

  1. Suppose an is a sequence with limn,,,an = b. Show that an = b2. That is, show that for any e > 0 there is an index M such that for any n > M it is true that lan2 — b21 < E. (Hint You may find Proposition 2 in Lecture 09-01, the identity x2 – y2 = (x y) ix y), and the triangle inequality Ix + yl < lx1+ lyl are useful here.)

Sample Solution