Difference between revisions of "Northeastern WOOTers Mock AIME I Problems/Problem 7"
(Created page with "== Problem 7 == Find the value of <cmath>\sum_{n=0}^{100}\left\lfloor\frac{3n+4}{13}\right\rfloor-\left\lfloor\frac{n-28+\left\lfloor\frac{n-7}{13}\right\rfloor}{4}\right\rfl...") |
(→Solution) |
||
| (3 intermediate revisions by the same user not shown) | |||
| Line 6: | Line 6: | ||
| + | == Solution == | ||
As of now, | As of now, | ||
| Line 12: | Line 13: | ||
<cmath>\sum_{n=0}^{100}\left\lfloor\frac{n-28+\left\lfloor\frac{n-7}{13}\right\rfloor}{4}\right\rfloor = 588</cmath> | <cmath>\sum_{n=0}^{100}\left\lfloor\frac{n-28+\left\lfloor\frac{n-7}{13}\right\rfloor}{4}\right\rfloor = 588</cmath> | ||
| − | Giving an answer of | + | Giving an answer of 562. |
| + | |||
| + | |||
| + | (Thread: https://artofproblemsolving.com/community/c5h2020524_floor_function_problem_mock_aime) | ||
Latest revision as of 22:52, 2 March 2020
Problem 7
Find the value of ![\[\sum_{n=0}^{100}\left\lfloor\frac{3n+4}{13}\right\rfloor-\left\lfloor\frac{n-28+\left\lfloor\frac{n-7}{13}\right\rfloor}{4}\right\rfloor.\]](http://latex.artofproblemsolving.com/d/5/0/d50a2d431c19da14a1315bafce20a96fbad235af.png)
Solution
As of now,
![\[\sum_{n=0}^{100}\left\lfloor\frac{3n+4}{13}\right\rfloor = 1150\]](http://latex.artofproblemsolving.com/a/6/4/a6430848e9683c7e907b908905b8f2ada57b8b19.png)
![\[\sum_{n=0}^{100}\left\lfloor\frac{n-28+\left\lfloor\frac{n-7}{13}\right\rfloor}{4}\right\rfloor = 588\]](http://latex.artofproblemsolving.com/6/6/c/66c5bd79519aacf96f7f8ecc15805f5264e81e60.png)
Giving an answer of 562.
(Thread: https://artofproblemsolving.com/community/c5h2020524_floor_function_problem_mock_aime)
