Question

Compute \frac{3}{4}\cdot \frac{8}{9}\cdot \frac{15}{16}\cdot \frac{24}{25}\cdot \frac{35}{36}\cdot \frac{48}{49}\cdot \frac{63}{64}\c.... Express your answer in the simplest way possible.

Answer 1

\[\frac{3}{4}\cdot \frac{8}{9}\cdot \frac{15}{16}\cdot \frac{24}{25}\cdot \frac{35}{36}\cdot \frac{48}{49}\cdot \frac{63}{64}\]

Answer 2

Latex doesn't work!!

Answer 3

fix'd that for you

Answer 4

It's
\[\prod_{i=1}^\infty \dfrac{i^2+2i}{i^2+2i+1} \]

Answer 5

ok then

Answer 6

let check:
i =1, then, numerator = 3, denominator = 4
i =2, then , numerator = 8, denominator =9
i =3, then numerator = 15, denominator =16
and so on.
the \(\prod\) stands for multiplication, right? , then it works well. hihihi

Answer 7

Oooops! That's a clever and sophisticated approach.

Another way (and a good check) would be to cancel everywhere possible in this fraction. For example, that 8 in the numerator, divided into that 16 in the denom., results in a 2 in the denom. And so on.