Question

Find S11 for 1 + 2 + 4 + 8 + …

Answer 1

Answer:

2,047

Step-by-step explanation:

Given:

$1+2+4+8+...$

Find:

$S_{11}$

You are given the geometric sequence. From the given sum, you can see that

$b_1=1\\ \\b_2=2=1\cdot 2=b_1\cdot 2\\ \\b_3=4=2\cdot 2=b_2\cdot 2\\ \\b_4=8=4\cdot 2=b_3\cdot 2\\ \\....\\ \\r=2$

To find the sum $S_{11},$ use formula

$S_n=\dfrac{b_1(1-r^n)}{1-r}$

Hence,

$S_{11}=\dfrac{1\cdot (1-2^{11})}{1-2}=\dfrac{1-2,048}{-1}=2,047$