+118667 To do this question it is easier to work backwards from the qanswers.
Take the first answer.
\(\displaystyle\sum_{j=1}^7 \frac{1}{2}(j+1)\\ When\;\; j=1\quad \text{The first term is }\quad \frac{1}{2}(1+1)=1 \quad \text {that is good}\\ When \;\; j=2\quad \text{The second term is }\quad \frac{1}{2}(2+1)=\frac{3}{2}= \quad \text {that is no good}\\\)
So it is not the first one.
If you think about it, the bottom of the fractions are \(2^0,2^1,2^2,....\) and the top is just 1. So the bottom is a power of 2.
Which out of the 4 seems likely?
Test that one, like I tested the first one, and see if it works.
So what is the answer? 
Please no one answer over me.
+118667 Yes that becasue you need to think about my answer.
Not everything in life is instant!
Have you worked through how I looked at the first possibility and then dismissed it as wrong?
+118667 Well have you tested either of them to see which one is right ?
Take the last one.
\(2^{j-1}\)
1) when j =1 what is the value?
2) when j=2 what is the value?
3) when j=3 waht is the value?
I want you to give me the answers to these questions.
Is this the right sequence?
