Basic Mathematics2081.25 marksNumerical: series convergence testComparison tests
Determine whether the series sumn=1infty frac52n2 + 4n + 3 is convergent or divergent.
Determine whether the series $\sum_{n=1}^{\infty} \frac{5}{2n^2 + 4n + 3}$ is convergent or divergent. [5]
- Series: $\displaystyle\sum{n=1}^{\infty} an$ where $an = \dfrac{5}{2n^2 + 4n + 3}$ - All terms positive for $n \geq 1$ (numerator and denominator positive). Choose the Limit Comparison Test. For large $n$, the dominant term in the denominator is $2n^2$, so $an$ behaves like $\dfrac{5}{2n^2}$. C...