Question

Part 2A This part is due on Monday 25 t March, electronic submission) Question 2.1 Approximate v171 as the continued fraction i.e. Compute the integers n, 2, and g 4 marks Question 2.2 Evaluate the following binomial coefficients a) (1) (b) (1) (c) (カ 6 marks) Part 2B (This part is due on Monday 1t April, electronic submission) Question 2.3 As his first step in proving an equation relating the infinite series for π/4 to the continued fraction for 4/r. Euler used the identity Prove this identity 6 marks Question 2.4 Find all r such that 3 (mod 7) 5 (mod 13) 17 (mod 23). 4 marks

Answer 1

Solulion 2.) APPsoximate Λ,1 a% the continued Psact on 2 13 <ほ1 <14 uos vg on both side 2. S0 2

Hence, J 13 + 13-t 26 2 Evaluate the oloiv binomial coeflidents 3 3 KEIN 2

3 2 27 IX2X3 21 XG 3 f 62 3 נ0,049382 子16 3 625 2u S04 625 24

SO 5000 รี) -0.0336 5 I yl 구, 구 -25-32 구 5 I 子5xsi 633600 63360O 16807X(20 633600 2016, 840 0.3141sy816 4万/t