Analysis
Problems related to calculus, limits, series, etc.
Problems in this category
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
The problem asks to graph the function $f(x) = x^3 - 4$.
Graphing FunctionsCubic FunctionsTransformationsVertical Translation
2025/3/6
We are asked to evaluate the infinite sum $\sum_{k=2}^\infty \left( \frac{3}{(k-1)^2} - \frac{3}{k^2...
Infinite SeriesTelescoping SeriesLimits
2025/3/6
The problem asks us to evaluate the infinite sum $\sum_{k=1}^{\infty} \frac{4^{k+1}}{7^{k-1}}$.
Infinite SeriesGeometric SeriesConvergence
2025/3/6
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