This is a very simple problem, but my answer is different from the answer sheet and I can't understand what I did wrong. Do I get something fundamentally wrong or the answer sheet be wrong?
According to an ancient belief, when a friend visits a sick person, 1/60 of his or her illness is taken away. How many friends need to visit to take away at least 99% of a person's illness?
To solve this problem, I made this table: $$1 ---> 1/60$$ $$ x ---> 0.99$$ from above, I got $x*(1/60)=1*0.99$. Then $x=0.99*60=59.4$. This means that 60 friends need to visit to take away at least 99% of a person's illness. But the answer sheet says 275, not 60.
Suppose the person starts with one whole illness ($1.0$). Then the first person visits. He now has $\frac{59}{60}$ of his illness remaining. Now the second person visits. He will then have $\frac{59}{60} \times \frac{59}{60}$ of his illness remaining (the second person takes away $\frac{1}{60}$ of how much illness he had before the second friend visited). So you see after the $n$th person visits, he will have $\frac{59}{60}^n$ of his illness remaining. You need to find the smallest $n$ so that $\frac{59}{60}^n \le 0.01$. You can use logarithms to solve this, if you've learned them. Otherwise you can try guess and check.