Question

Remarks: Any fraudulent attempt will be penalized by the cancellation of the ex Make your solving method clear in order to evaluate it if the resuts are in Read the whole exam before starting solving the problems Problem 130 pts) 1. Show that for every n e N* and for any number z é C, we have: (z-)1+z+z)-zt-1 Deduice that if z#1, we have: 1++-(zhD/z 1) 2. Verify that for every xeR we have ex-I = 2ier 2sin(x/2). 3. Let neiM Calculate for every rER the following sum: Then deduce the values of x,-1-cos(x)+cos(2x)+ +cos((n-1)x) Kn = sin(x)+sin(2x)+-..+3111( (n-l )x)

Answer 1

いーリ 2 į叭 Ca s2n 2 1 (n/h

3 Sute e e. Cos inm)