Difference between revisions of "2018 AMC 8 Problems/Problem 2"
The referee (talk | contribs) (→Problem 2) |
|||
| Line 3: | Line 3: | ||
<math>\textbf{(A) }\frac{7}{6}\qquad\textbf{(B) }\frac{4}{3}\qquad\textbf{(C) }\frac{7}{2}\qquad\textbf{(D) }7\qquad\textbf{(E) }8</math> | <math>\textbf{(A) }\frac{7}{6}\qquad\textbf{(B) }\frac{4}{3}\qquad\textbf{(C) }\frac{7}{2}\qquad\textbf{(D) }7\qquad\textbf{(E) }8</math> | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | You may simply the expression to get <math>\frac{2}{1} \cdot \frac{3}{2} \cdot \frac{4}{3} \cdot \frac{5}{4} \cdot \frac{6}{5} \cdot \frac{7}{6}</math>. | ||
| + | |||
| + | Using telescoping, many things cancel out. You are left with <math>\frac{7}{1}</math> which is equivelant to <math>7</math>, or <math>\textbf{(D) }</math> | ||
==See Also== | ==See Also== | ||
Revision as of 12:02, 21 November 2018
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
You may simply the expression to get 
.
Using telescoping, many things cancel out. You are left with 
which is equivelant to 
, or 
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. 
