Math 251H Project #3 This assignment is due on Friday, April 19, 2024 The purpose of this project is develop another convergence test. Here is the set-up: Suppose that for each n 2 1, an > 0 and an Z an+1. 1. Prove that >an converges if 2" a2n converges. n=1 n= 0 Note that > 2" a2n = a1 + 2a2 + 404 + 8as + 16016 + . .. n= 0 2. Prove that > an diverges if ) 2" a2n diverges. n=1 n= 0 3. Use #1 and #2 to show that converges if and only if p > 1. n = 1 4. Use #1 and #2 to show that n(Inn)p 5 converges if and only if p > 1. n =2