Question

Find S11 for 1 + 2 + 4 + 8 + …

Answer 1

2,047

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=(b_1(1-r^n))/(1-r)`

Hence,

`S_(11)=(1\cdot (1-2^(11)))/(1-2)=(1-2,048)/(-1)=2,047`