Northeastern WOOTers Mock AIME I Problems/Problem 7
Revision as of 22:28, 2 March 2020 by Professor-mom (talk | contribs) (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...")
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)
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 662.
