Basic Mathematics20795 marksNumerical: series convergence divergenceConvergence and divergence of series
Determine whether the following series are convergence or divergence sumn=1infty frac55n-1, sumn=0infty frac1n!.
Determine whether the following series are convergence or divergence $\sum_{n=1}^{\infty} \frac{5}{5n-1}$, $\sum_{n=0}^{\infty} \frac{1}{n!}$. [5]
- Series 1: $\displaystyle \sum{n=1}^{\infty} \frac{5}{5n-1}$ - Series 2: $\displaystyle \sum{n=0}^{\infty} \frac{1}{n!}$ --- Step 1 - Divergence (nth term) test. $$\lim{n \to \infty} \frac{5}{5n-1} = 0$$ The nth term tends to $0$, so this test is inconclusive. Step 2 - Limit Comparison Test with...