Tricky fractions
Use this series of fractions to find the value of x.
Problem
Student Solutions
Anwser: 341
Image

Image

The first pair of terms add up to $\dfrac{1}{2}-\dfrac{1}{4}=\dfrac{1}{4}$
Image

Image

The next pair of terms add up to $\dfrac18-\dfrac1{16}=\dfrac{1}{16}$
Image

The next pair of terms ($\frac1{32}-\frac1{64}$) add up to $\dfrac1{64}$
... the last pair of terms add up to $\frac1{1024}$
The whole sum is $\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}+\dfrac{1}{1024}$
Common denominator: $1024$
Each fraction is $4$ times smaller than the last so whole sum is equal to
$\dfrac{256+64+16+4+1}{1024}=\dfrac{341}{1024}$
Multiplying the sequence by 2
If