Test whether the series sumn=2infty frac2n2 - 1 converges or diverges. | Basic Mathematics 2081

Basic Mathematics20815 marksNumerical: series convergence testComparison tests

Test whether the series $\sum_{n=2}^{\infty} \frac{2}{n^2 - 1}$ converges or diverges. [5]

Series: $\displaystyle\sum{n=2}^{\infty} \frac{2}{n^2-1}$ - Starting index: $n = 2$ - Task: determine convergence/divergence (and sum if convergent). Partial fractions. $n^2 - 1 = (n-1)(n+1)$ $\frac{2}{(n-1)(n+1)} = \frac{A}{n-1} + \frac{B}{n+1}$ $2 = A(n+1) + B(n-1)$ -

Series: $\displaystyle\sum{n=2}^{\infty} \frac{2}{n^2-1}$ - Starting index: $n = 2$ - Task: determine convergence/divergence (and sum if convergent). Partial fractions. $$n^2 - 1 = (n-1)(n+1)$$ $$\frac{2}{(n-1)(n+1)} = \frac{A}{n-1} + \frac{B}{n+1}$$ $$2 = A(n+1) + B(n-1)$$ -