MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

Riemann sum limit for x^k integral

1175BeginnerCalculusSeries

OME 12

Calculate the limit $$\lim_{n \rightarrow \infty} \frac{1}{n}\left(\frac{1}{n^{k}}+\frac{2^{k}}{n^{k}}+\cdots+\frac{(n-1)^{k}}{n^{k}}+\frac{n^{k}}{n^{k}}\right).$$ (To compute the limit, one may follow the procedure of constructing an integral.)
0 students attempted0% solvedRating 1175

Related practice paths

AMC 12 PracticeAdvanced high school contest practice and review.AMC 10 vs AMC 12Choose the right practice path and difficulty level.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 Hints

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.