grandes-ecoles 2025 Q6

grandes-ecoles · France · mines-ponts-maths2__psi Sequences and series, recurrence and convergence Convergence proof and limit determination

Express $f ( 0 )$ and $\lim _ { x \rightarrow + \infty } f ( x )$ in terms of $a _ { 0 }$ and $b _ { 0 }$.
Here $f = \sum_{n\geq 0} f_n$ is the sum of a Dirichlet series with $f_n(x) = a_n e^{-\lambda_n x}$, $\lambda_0 = 0$, and $b_0 = \sum_{n=1}^{+\infty} a_n$.

Express $f ( 0 )$ and $\lim _ { x \rightarrow + \infty } f ( x )$ in terms of $a _ { 0 }$ and $b _ { 0 }$.

Here $f = \sum_{n\geq 0} f_n$ is the sum of a Dirichlet series with $f_n(x) = a_n e^{-\lambda_n x}$, $\lambda_0 = 0$, and $b_0 = \sum_{n=1}^{+\infty} a_n$.

Paper Questions

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