Useful shortcut

Algebra Level 1

If $f(x)=\frac{1}{x}+1,$ find $\prod_ {k=1} ^{2018} f(k) =f(1) \times f(2) \times f(3)\times \cdots\times f(2017)\times f(2018).$

The answer is 2019.

1 solution

Diego Perez
Apr 30, 2018

We have: $f(x)=\frac{1}{x}+1 =\frac{1+x}{x}$ , so

$f(1) \times f(2) \times f(3)\times \cdots\times f(2017)\times f(2018)=\frac{2}{1}\times \frac{3}{2}\times \frac{4}{3}\times \cdots \times \frac{2019}{2018} =\frac{2019}{1}=\boxed{2019}$

Useful shortcut

The answer is 2019.

1 solution

0 pending reports