Show that the series converges. | Mathematics I 2077

Mathematics I20775 marksNumerical: Series convergenceConvergence tests and power series

Show that the series converges. $\sum_{n=0}^{\infty} \frac{1}{1+n^2}$ [5]

Show that the series converges. $$\sum_{n=0}^{\infty} \frac{1}{1+n^2}$$ [5]

Series to test: $\sum{n=0}^{\infty} \frac{1}{1+n^2}$ Term: $an = \dfrac{1}{1+n^2}$ , starting at $n = 0$ . No numerical parameters missing; this is an analytical convergence proof. --- Integral Test: If $f$ is continuous, positive, and decreasing on $[1,\infty)$ with $an = f(n)$ , then $\sum an$ c...

Series to test: $$\sum{n=0}^{\infty} \frac{1}{1+n^2}$$ Term: $an = \dfrac{1}{1+n^2}$, starting at $n = 0$. No numerical parameters missing; this is an analytical convergence proof. --- Integral Test: If $f$ is continuous, positive, and decreasing on $[1,\infty)$ with $an = f(n)$, then $\sum an$ c...

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