1. Begin with the Taylor series cos x = 1 - 2! 4! + + and mimic Euler's work 6! (i.e. equate this infinite sum with an infinite product) to derive the sum of the recip- rocals of the squares of the odd integers: 1 1 1 1 1+=+ + + + ...= 9 25 49 81 77 8 2. (a) Using the great theorem from this chapter and the result from question 1, evaluate 1 1 the alternating series 1 1 1 + + 4 9 16 25 (b) Use the product expension of cos x from question 1 to show 2 2 2 6 6 10 10 14 14... 1.3.5.7.9 11 13 15..