MATH 113 Midterm: MATH 113 Harvard 113 Fall 01113hw1
Document Summary
Show all your work, and write up your solutions as neatly as possible. See the course syllabus for the cooperation policy on homeworks. You may use any formulas which are stated in chapters 1 and 2 of the book, even if we did not speci cally discuss them in class. 1 zw| = 1: suppose p c[x, y] is a polynomial in both x + iy and x iy. Show that p is constant: let p c[z] be a nonconstant analytic polynomial. Let = cos( ) 1, = sin( ), = cos((n + 1) ) 1, = sin((n + 1) ). 2 + 2: suppose {an} is a sequence of positive real numbers and. 1 + cos + cos2 + + cosn = lim n an+1 an. Show that limn a1/n n = l. use this to nd the radius of convergence of.
