Respuesta :

LammettHash
[tex]S=\displaystyle\sum_{n=1}^7\left(\frac14\right)^n[/tex]

[tex]\displaystyle S=\frac14+\left(\frac14\right)^2+\cdots+\left(\frac14\right)^7[/tex]
[tex]\displaystyle\frac14S=\left(\frac14\right)^2+\left(\frac14\right)^3+\cdots+\left(\frac14\right)^8[/tex]
[tex]\displaystyle S-\frac14S=\frac14+\left(\left(\frac14\right)^2-\left(\frac14\right)^2\right)+\cdots+\left(\left(\frac14\right)^7-\left(\frac14\right)^7\right)-\left(\frac14\right)^8[/tex]
[tex]\displaystyle\frac34S=\frac14-\left(\frac14\right)^8[/tex]
[tex]\displaystyle S=\frac{\frac14-\left(\frac14\right)^8}{\frac34}=\frac{5461}{16384}[/tex]

Otras preguntas