Question

Nu stiu sa rezolv problema!Ajutatima!

Answer 1

[tex]\text{Pnetru inceput sa rezolvam suma din paranteza.O voi nota cu S.}\\ S=1+\dfrac{1}{2}+\dfrac{1}{2^2}+\ldots+\dfrac{1}{2^{2017}}|\cdot \dfrac{1}{2}\\ \dfrac{1}{2}S=\dfrac{1}{2}+\dfrac{1}{2^2}+\ldots+\dfrac{1}{2^{2018}}\\ ------------\\ S-\dfrac{1}{2}S=1-\dfrac{1}{2^{2018}}\\ \dfrac{1}{2}S=1-\dfrac{1}{2^{2018}}\\ S=\dfrac{2^{2018}-1}{2^{2017}}}[/tex]
[tex]\text{Revenind la exercitiu:}\\ x:\dfrac{2^{2018}-1}{2^{2017}}=\dfrac{2^{2016}}{2^{2018}-1}\\ x\cdot \dfrac{2^{2017}}{2^{2018}-1}=\dfrac{2^{2016}}{2^{2018}-1}\\ x\cdot 2^{2017}=2^{2016}\\ \boxed{x=\dfrac{1}{2}}[/tex]