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Browse Classroom Capsules and Notes

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Displaying 1101 - 1110 of 1214

The author uses the Stolz-Cesàro theorem to compute the sums of the integer powers.

Synthetic division is generalized from linear divisors to general polynomial divisors.

Experiments show that people tend to behave "unfairly" in the fair R-P-S games. The authors find the optimal strategies for two cases.

In solving an interesting geometric problem, the author shows again the two important steps in applying Ceva's Theorem.

Golomb's theorem on \(x/\pi(x)\) about prime number distribution is generalized and has a new proof.

The author describes two methods that Fibonacci might have used to find an approximate solution to a cubic equation posed in the court of the Holy Roman Emperor, Fredrick II in 1225.

Without using double integrals, a new method is presented to evaluate the two Fresnel integrals about sine and cosine that has a wider applications than previous methods.
Two conjectures on summations involving binomial coefficients are proved as a consequence of a more general combinatorial identity.
The author introduces two methods of solving linear equations used by ancient Egyptians and Chinese that is also related to Cramer's rule.
The derivative of arctangent is derived directly from the definition of derivative by using some clever inequalities.

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