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Browse Classroom Capsules and Notes

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Displaying 1061 - 1070 of 1135

In this note an elementary proof of Stirling's asymptotic formula for \(n!\) is given.

A covering system is a system of \(k\) arithmetic progressions whose union includes all integers. This paper presents upper bounds on the number of consecutive integers which need to be checked...

The authors explain certain inequalities visually.

A Fibonacci identity is depicted visually.

The authors study the upper bound for the expected differences between order statistics of a distribution.

Using just very basic knowledge of finite fields and the inclusion-exclusion formula, the authors show how one can see the shape of Gauss` formula for the number of irreducible polynomials of...

An inductive proof is presented for the bounds of the remainder of Taylor expansion. This result, with Darboux's theorem, implies the classical formula for the remainder.

This article uses four different methods to evaluate a type of Poisson integral: Riemann sums, functional equation, parametric differentiation, and infinite series.

A discrete analog of integration by parts

An application for integration

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