What is the value of the expression: $(1+\frac 12)(1+\frac 13)(1+\frac 14)...(1+\frac {1}{2004})(1+\frac {1}{2005})$? This question appeared on the UKMT senior maths challenge 2005, and I can't find an adequate method for a solution given its context i.e. without a calculator, and it should only take 3 to 4 minutes. I'm sure I'm missing something obvious.
Thanks!
Tuesday, May 14, 2019
algebra precalculus - What is the value of the expression: $(1+frac 12)(1+frac 13)(1+frac 14)...(1+frac {1}{2004})(1+frac {1}{2005})$?
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