Question

Calculati 1 supra 2 - ( 1 supra 2 la puterea a doua + 1 supra 2 la puterea a treia +...+ 1 supra 2 la puterea a zecea ) . Multumesc !

Answer 1

notezi S =(1/2)^2 +(1/2)^3+...+(1/2)^10
=> 1/2 *S =             (1/2)^3+..+(1/2)^10+(1/2)^11
=======================================sacadem S-(1/2)*S =>
=> 1/2 *S =(1/2)^2-(1/2)^11 =>
=> S =1/2 - (1/2)^10 =>
=> 1/2 -S = 1/2 -(1/2 -(1/2)^10)=(1/2)^10