Question

Calculati : ( 1+2+2 la puterea 2 + ... + 2 la puterea 99 ) : ( 2 la puterea 100 - 1 )

Answer 1

[tex]A=(1+2+2^2+2^3+...+2^{99}):(2^{100}-1)\\ Luam\ prima\ suma\ separat:\\ B=1+2+2^2+....+2^{99}|*(-2)\\ -2B=-2-2^2-...-2^{100}\\ ............................................\\ -B=1-2^{100}=\ \textgreater \ B=2^{100}-1\\ Revenim\ la\ exercitiu:\\ A=(2^{100}-1):(2^{100}-1)=\ \textgreater \ A=1[/tex]