Answer:
2,047
Step-by-step explanation:
Given:
[tex]1+2+4+8+...[/tex]
Find:
[tex]S_{11}[/tex]
You are given the geometric sequence. From the given sum, you can see that
[tex]b_1=1\\ \\b_2=2=1\cdot 2=b_1\cdot 2\\ \\b_3=4=2\cdot 2=b_2\cdot 2\\ \\b_4=8=4\cdot 2=b_3\cdot 2\\ \\....\\ \\r=2[/tex]
To find the sum [tex]S_{11},[/tex] use formula
[tex]S_n=\dfrac{b_1(1-r^n)}{1-r}[/tex]
Hence,
[tex]S_{11}=\dfrac{1\cdot (1-2^{11})}{1-2}=\dfrac{1-2,048}{-1}=2,047[/tex]
