Difference between revisions of "2018 AMC 8 Problems/Problem 2"
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Using telescoping, most of the terms cancel out diagonally. We are left with <math>\frac{7}{1}</math> which is equivalent to <math>7</math>. Thus the answer would be <math>\boxed{\textbf{(D) }7}</math>. | Using telescoping, most of the terms cancel out diagonally. We are left with <math>\frac{7}{1}</math> which is equivalent to <math>7</math>. Thus the answer would be <math>\boxed{\textbf{(D) }7}</math>. | ||
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Revision as of 15:55, 27 October 2019
Problem 2
What is the value of the product![\[\left(1+\frac{1}{1}\right)\cdot\left(1+\frac{1}{2}\right)\cdot\left(1+\frac{1}{3}\right)\cdot\left(1+\frac{1}{4}\right)\cdot\left(1+\frac{1}{5}\right)\cdot\left(1+\frac{1}{6}\right)?\]](http://latex.artofproblemsolving.com/2/c/7/2c7aacf4c691c580906f1aaa847be38a7dbf6f26.png)
Solution
By adding up the numbers in each parentheses, we have: 
.
Using telescoping, most of the terms cancel out diagonally. We are left with 
which is equivalent to 
. Thus the answer would be 
.
