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The problem asks to find the $y$-intercept of a line, given that the slope of the line is $2$. The s...
Linear EquationsY-interceptSlope
2025/3/7
The problem asks us to find the slope and y-intercept of a line from its graph and then use these to...
Linear EquationsSlopeY-interceptGraphing
2025/3/7
The problem asks us to find the slope and y-intercept of the given line and then write the equation ...
Linear EquationsSlope-Intercept FormCoordinate Geometry
2025/3/7
(1) 1から100までの整数のうち、3と互いに素なものの個数、10と互いに素なものの個数、30と互いに素なものの個数を求める。 (2) 和が2で積が$2-a$となる2つの異なる整数が存在するような自...
整数互いに素数列三角関数微分
2025/3/7
The problem is to find the sum of the infinite series $\sum_{k=1}^{\infty} \frac{1}{k^3}$.
Infinite SeriesRiemann Zeta FunctionApery's Constant
2025/3/7
The problem asks us to determine if the series $\sum_{k=1}^{\infty} k \sin \frac{1}{k}$ converges or...
Series ConvergenceLimit TestDivergence TestLimitsTrigonometric Functions
2025/3/7
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 us to determine whether the following equations are true or false: 1. $3^5 = 3 \tim...
ExponentsEvaluationComparison
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