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Question 503514: What is the value of (1+1/2)(1+1/3)(1+1/4)...(1+1/2011)? choose the answer and explain the reason to choose your response
1005
2011
1006
2012
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! (1+1/2)(1+1/3)(1+1/4)(1+1/5)(1+1/6)...(1+1/2011)
(2/2+1/2)(3/3+1/3)(4/4+1/4)(5/5+1/5)(6/6+1/6)...(2011/2011+1/2011)
(3/2)(4/3)(5/4)(6/5)(7/6)...(2012/2011)
Notice in the last step, there's a 3 in the first numerator and a 3 in the second denominator. These terms will cancel. Also, there's a 4 in the second numerator and a 4 in the third denominator. These terms will cancel too. The basic pattern is that any given numerator will cancel with the the denominator in the next fraction
All this cancelling leaves us with
(1/2)(1/1)(1/1)(1/1)(1/1)...(2012/1)
which collapses to (1/2)(2012/1) and that multiplies and simplifies to 2012/2 = 1006
So the answer is choice C
If you need more help, feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html
Thanks,
Jim
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