Difference between revisions of "2018 AMC 8 Problems/Problem 2"
Winterowl23 (talk | contribs) m (→Solution) |
|||
| Line 1: | Line 1: | ||
| − | ==Problem | + | ==Problem== |
What is the value of the product<cmath>\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)?</cmath> | What is the value of the product<cmath>\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)?</cmath> | ||
Revision as of 12:49, 18 January 2021
Problem
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 of the 
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 
.
See also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
