Basic Mathematics20805 marksNumerical: integral test convergenceIntegral test
State integral test and apply it to test the convergence of the series sumn=1inftyfrac1n2+1.
State integral test and apply it to test the convergence of the series $\sum_{n=1}^{\infty}\frac{1}{n^2+1}$. [5]
- Series: $\displaystyle\sum{n=1}^{\infty}\frac{1}{n^2+1}$ - Associated function: $f(x)=\dfrac{1}{x^2+1}$, tested on $[1,\infty)$ Let $f(x)$ be a function that is continuous, positive, and monotonically decreasing on $[1,\infty)$, and suppose $f(n)=an$ for the terms of the series $\sum an$. Then:...