# SOLUTION: 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

Algebra ->  Algebra  -> Expressions -> SOLUTION: 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       Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Evaluation of expressions, parentheses Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on expressions 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(28476)   (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