Homework Help

Show that  1/ log_2 2001 + 1/ log_3 2001 + 1/ log_4 2001...

user profile pic

roshan-rox | Valedictorian

Posted July 7, 2013 at 6:35 PM via web

dislike 0 like

Show that 

1/ log_2 2001 + 1/ log_3 2001 + 1/ log_4 2001 +................................+ 1/ log_100  2001                        = 1/ log_100! 2001 

1 Answer | Add Yours

user profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 7, 2013 at 6:55 PM (Answer #1)

dislike 1 like

We know that;

`log_ab = 1/(log_ba)`

`1/(log_2(2001))+1/(log_3(2001))+1/(log_4(2001))+.......+1/(log_100(2001))`

`= log_(2001)2+log_(2001)3+log_(2001)4+......+log_(2001)100`

`= log_(2001)(2xx3xx4.....100)`

`= log_(2001)(1xx2xx3......xx100)`

`= log_(2001)(100!)`

`= 1/(log_(100!)2001)`

 

So the answer is obtained as required.

`1/(log_2(2001))+1/(log_3(2001))+1/(log_4(2001))+.......+1/(log_100(2001)) = 1/(log_(100!)2001)`

 

 

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes