Question

1\(\dfrac{1}{12}\) x 1\(\dfrac{1}{13}\) x 1\(\dfrac{1}{14}\) x 1\(\dfrac{1}{15}\) x ... x 1\(\dfrac{1}{2005}\) x 1\(\dfrac{1}{2006}\) x 1\(\dfrac{1}{2007}\)

Answer 1

=13/12x14/13x15/14x16/15x...x2006/2005x2007/2006x2008/2007

=2008/12

=502/3

Answer 2

A = 1\(\dfrac{1}{12}\) \(\times\) 1\(\dfrac{1}{13}\) \(\times\) 1\(\dfrac{1}{14}\) \(\times\) 1\(\dfrac{1}{15}\) \(\times\) ... \(\times\) 1\(\dfrac{1}{2005}\) \(\times\) 1\(\dfrac{1}{2006}\) \(\times\) 1\(\dfrac{1}{2007}\)

A = ( 1 + \(\dfrac{1}{12}\)) \(\times\) ( 1 + \(\dfrac{1}{13}\)) \(\times\) ( 1 + \(\dfrac{1}{14}\)) \(\times\)...\(\times\) ( 1 + \(\dfrac{1}{2006}\))\(\times\)(1+\(\dfrac{1}{2007}\))

A = \(\dfrac{13}{12}\) \(\times\) \(\dfrac{14}{13}\) \(\times\) \(\dfrac{15}{14}\) \(\times\) ...\(\times\) \(\dfrac{2007}{2006}\) \(\times\) \(\dfrac{2008}{2007}\)

A = \(\dfrac{13\times14\times15\times...\times2007}{13\times14\times15\times...\times2007}\) \(\times\) \(\dfrac{2008}{12}\)

A = 1 \(\times\) \(\dfrac{502}{3}\)

A = \(\dfrac{502}{3}\)