So I was given a question that said : A person has 2/3 of a cake in the fridge, and to make it last longer, they decide to only eat half of what was left each day. If this person has a serving each day, how much of the cake have they eaten?
I assumed that the common ratio between each amount every day was 1/2. So therefore, after every serving, half of the previous amount would be left. So if servings are X and amount left is Y, then for X = 1, Y should be 1/3. And so forth. My answer so far was that she had eaten 47/48 of the cake by the 5th serving. Is this correct?
EDIT : To be clear, the starting amount of the cake is 2/3. The person eats 1/2 of what was there before each serving. So for the first serving, they eat 1/3 (half of 2/3). The next serving, they eat half of 1/3.
After $n$ servings, what is left is $\frac{2}{3}\frac{1}{2^n}$. What the person ate is $\frac{2}{3}-\frac{2}{3}\frac{1}{2^n}$. Your answer assumes that the first $1/3$ of the cake was also eaten by these people. You did $1-\frac{2}{3}\frac{1}{2^n}$.