Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
The problem is to find the sum of the infinite series $\sum_{k=1}^{\infty} (\frac{e}{\pi})^{k+1}$.
Infinite SeriesGeometric SeriesConvergence
2025/3/6
We are asked to find the sum of the infinite series $\sum_{k=1}^{\infty} (\frac{e}{\pi})^{k+1}$.
Infinite SeriesGeometric SeriesConvergence
2025/3/6
We are asked to evaluate the infinite sum $\sum_{k=1}^{\infty} \frac{2}{(k+2)k}$.
Infinite SeriesTelescoping SeriesPartial Fraction Decomposition
2025/3/6
We need to find the value of the infinite sum $\sum_{k=2}^{\infty} (\frac{1}{k} - \frac{1}{k-1})$.
Infinite SeriesTelescoping SeriesLimits
2025/3/6
We need to find the indefinite integral of $e^{2x} \sin x$ with respect to $x$.
IntegrationIntegration by PartsIndefinite IntegralExponential FunctionTrigonometric Function
2025/3/6