MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

Convergent Sum with Radical Entries

2550MasterCalculusSeries

Brazilian Math Olympiad

Let $N = 2012$. Find all $N^2$-uples of real numbers $a_{i,j}$, $1 \le i, j \le N$, such that the following limit is convergent: $$ \lim_{x \to +\infty} \sum_{1 \le i,j \le N} \left(a_{i,j} \sqrt[j]{x+i}\right) $$
0 students attempted0% solvedRating 2550

Related practice paths

Olympiad-Style PracticeDeep contest practice for proof-style problem solving.How to Qualify for AIMEScore goals, contest choice, and prep habits for AIME hopefuls.How to Review Missed AMC ProblemsTurn missed problems into a repeatable improvement loop.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints5

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions1

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.