Hi.

Q.1   I have a doubt here. Your question is not clear. Please rewrite.

 

Q.2 The equation you get will be

                     4*[ 1- (3/4)ⁿ ] - 4 < 1 / 10⁶

              Now,

                      After doing manipulation you get :

                   4*[(3/4)ⁿ ] > (1 / 10⁶ )

           The only problem i am getting is solving this. Even if i use hit and trial

             i am not able to get the answer. And i don't think i have done anything wrong. Please try or let other people answer. Even i will vist this post after some time.

 

Q.3      C₀ + xC₁ + .......................... + xⁿC_n = (1+x)ⁿ

           Put x =1 :

            C₀ + C₁ + .......................... + C_n = 2ⁿ

        Put x = -1 :

                C₀ - C₁ + .......................... + (-1)ⁿC_n = 2ⁿ

            Subtract both, divide the LHS,RHS by 2 and you get the answer.