Evaluate

Algebra Level 2

( 1 1 2 ) ( 1 1 3 ) ( 1 1 4 ) ( 1 1 n ) \left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\ldots\left(1-\frac{1}{n}\right)


Inspiration .
n n 1 none of the above. 0 1 n \frac {1}{n}

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Rohit Udaiwal
Sep 26, 2015

( 1 1 2 ) ( 1 1 3 ) ( 1 1 4 ) ( 1 1 ( n 2 ) ) ( 1 1 ( n 1 ) ) ( 1 1 n ) \color{#3D99F6}{\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\ldots\left (1-\frac {1}{(n-2)}\right)\left(1-\frac{1}{(n-1)}\right)\left(1-\frac{1}{n}\right)} = ( 1 2 ) ( 2 3 ) ( 3 4 ) ( n 3 n 2 ) ( n 2 n 1 ) ( n 1 n ) \color{#EC7300}{= \left (\frac {1}{2}\right)\left (\frac{2}{3}\right)\left (\frac {3}{4}\right)\ldots\left (\frac {n-3}{n-2}\right)\left (\frac {n-2}{n-1}\right)\left (\frac {n-1}{n}\right)} = 1 n \color{#20A900}{=\boxed {\frac {1}{n}}}

Try this

Nihar Mahajan - 5 years, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...