Respuesta :
The general form of a geometric series is the following:
[tex]u_n=u_1r^n[/tex] wherein u_n is the first term and r the ratio.
So,
[tex]u_n= \frac{1}{2} 3^n[/tex]
The sum of N first terms is given by the formula:
[tex]S_N=u_1 \frac{1-r^N}{1-r}\\= \frac{1}{2} \frac{1-3^N}{1-3}\\= -\frac{1}{4}(1-3^N) [/tex]
The number of terms is 5, so we get the formula:
[tex] -\frac{1}{4}(1-3^5)=62.5\\ -\frac{1}{4}(1-243)=62.5\\ -\frac{1}{4}(-242)=62.5\\ 60,5=62.5[/tex]
The sum is rather 60.5 than 62.5
[tex]u_n=u_1r^n[/tex] wherein u_n is the first term and r the ratio.
So,
[tex]u_n= \frac{1}{2} 3^n[/tex]
The sum of N first terms is given by the formula:
[tex]S_N=u_1 \frac{1-r^N}{1-r}\\= \frac{1}{2} \frac{1-3^N}{1-3}\\= -\frac{1}{4}(1-3^N) [/tex]
The number of terms is 5, so we get the formula:
[tex] -\frac{1}{4}(1-3^5)=62.5\\ -\frac{1}{4}(1-243)=62.5\\ -\frac{1}{4}(-242)=62.5\\ 60,5=62.5[/tex]
The sum is rather 60.5 than 62.5
