MATH 410 Study Guide - Midterm Guide: Pointwise Convergence, Uniform Convergence

• School: University of Maryland
• Department: Mathematics
• Course: MATH 410
• Professor: All

Document Summary

Suppose m is an upper bound for |f (n+1)| and. Use the lagrange remainder theorem to prove that. 4m (n + 2)! (1/3)n+2: let f and g be the series f (x) = Prove or disprove the following statement: f de nes a di erentiable function from (0, + ) into r whose derivative is de ned by the series g: suppose ak is a sequence of real numbers such that. Prove that the radius of convergence r of the series p (a) (15 points) if |x| < 1/ , then the series converges; (b) (10 points) if |x| > 1/ , then the series diverges. k=0 akxk is 1/ , by showing.