Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem is to evaluate the infinite sum $\sum_{k=1}^{\infty} (\frac{1}{k} - \frac{1}{k+1})$.
Infinite SeriesTelescoping SeriesLimitsSummation
2025/3/7
The problem asks to evaluate the infinite sum $\sum_{k=1}^{\infty} \frac{1}{k^3}$. This is Apéry's c...
Riemann Zeta FunctionInfinite SeriesApery's ConstantNumber Theory
2025/3/7
We need to determine the convergence or divergence of the infinite series $\sum_{k=1}^{\infty} \frac...
Infinite SeriesConvergencep-seriesRiemann Zeta Function
2025/3/7
The problem is to determine whether the series $\sum_{k=1}^{\infty} \frac{1}{k\sqrt{k}}$ converges o...
Infinite SeriesConvergencep-series
2025/3/7
We are asked to solve the second-order linear non-homogeneous differential equation $y'' - y' = 2 - ...
Differential EquationsSecond-Order Linear Non-Homogeneous Differential EquationsInitial Value Problem
2025/3/6
We need to solve the second-order linear non-homogeneous differential equation: $y'' + y = x^2 - x$.
Differential EquationsSecond-Order Linear Non-Homogeneous Differential EquationsMethod of Undetermined Coefficients
2025/3/6
The problem is to solve the second-order non-homogeneous linear differential equation: $y'' - 3y' = ...
Differential EquationsSecond-Order Differential EquationNon-homogeneous Differential EquationLinear Differential Equation
2025/3/6
The problem is to solve the second-order linear non-homogeneous ordinary differential equation: $y''...
Differential EquationsSecond-Order Linear Non-Homogeneous Ordinary Differential Equation
2025/3/6
The problem asks to evaluate the infinite sum $\sum_{k=2}^{\infty} \left( \frac{3}{(k-1)^2} - \frac{...
Infinite SeriesTelescoping SeriesLimits
2025/3/6
We need to evaluate the infinite sum $\sum_{k=2}^{\infty} \left( \frac{3}{(k-1)^2} - \frac{3}{k^2} \...
Infinite SeriesTelescoping SeriesLimitSummation
2025/3/6