Question

A=3+2+2^2+2^3+.....+2^50

 

Answer 1

A=3+(2+2^2+2^3+.....+2^50)

=> A-3=2+2^2+2^3+.....+2^50

=> 2.(A-3)=2^2+2^3+.....+2^51

=> 2(A-3)-(A-3)=A-3=(2^2+2^3+.....+2^51)-(2+2^2+2^3+.....+2^50)=2^51-2

=> A=2^51-2+3

Answer 2

A=3+(2+2^2+2^3+.....+2^50)

=> A-3=2+2^2+2^3+.....+2^50

=> 2.(A-3)=2^2+2^3+.....+2^51

=> 2(A-3)-(A-3)=A-3=(2^2+2^3+.....+2^51)-(2+2^2+2^3+.....+2^50)=2^51-2

=> A=2^51-2+3