Compute the following expression: $\prod^{99}_{i=10} \frac{i}{i+1}$

Question

I understand the rules for summation now. But not product notation. This is what I have so far. Not sure if it is correct.

Answer 1

$\require{cancel}$ $$\prod_{i=10}^{99}\frac{i}{i+1}=\frac{\prod_{i=10}^{99}i}{\prod_{i=10}^{99}(i+1)}$$ $$=\frac{\prod_{i=10}^{99}i}{\prod_{i=11}^{100}i}$$ $$=\frac{10\cdot\cancel{(\prod_{i=11}^{99}i)}}{\cancel{(\prod_{i=11}^{99}i)}\cdot 100}$$ $$=\frac{10}{100}$$ $$=\frac1{10}$$

Answer 2

Note that $11$ cancels between the first and second terms. Similarly, $12$ cancels between the second and third. Like a telescoping addition series, most of the terms cancel. You are left with ????