Difference between revisions of "Random Problem"
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| − | Problem | + | ==Problem== |
The sum<cmath>\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+\cdots+\frac{2021}{2022!}</cmath>can be expressed as <math>a-\frac{1}{b!}</math>, where <math>a</math> and <math>b</math> are positive integers. What is <math>a+b</math>? | The sum<cmath>\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+\cdots+\frac{2021}{2022!}</cmath>can be expressed as <math>a-\frac{1}{b!}</math>, where <math>a</math> and <math>b</math> are positive integers. What is <math>a+b</math>? | ||
<math>\textbf{(A)}\ 2020 \qquad\textbf{(B)}\ 2021 \qquad\textbf{(C)}\ 2022 \qquad\textbf{(D)}\ 2023 \qquad\textbf{(E)}\ 2024</math> | <math>\textbf{(A)}\ 2020 \qquad\textbf{(B)}\ 2021 \qquad\textbf{(C)}\ 2022 \qquad\textbf{(D)}\ 2023 \qquad\textbf{(E)}\ 2024</math> | ||
| + | ==Solution== | ||
| + | ??? | ||
Revision as of 19:15, 27 January 2023
Problem
The sum![\[\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+\cdots+\frac{2021}{2022!}\]](http://latex.artofproblemsolving.com/7/2/6/726b88e230d5c0a0303ef6ca7177fa73b7eec900.png)
can be expressed as 
, where 
and 
are positive integers. What is 
?
Solution
???
