(Solved): Question 17 Test the series for convergence or divergence using the Alternating Series Test. \[ \su ...

Question 17

Test the series for convergence or divergence using the Alternating Series Test. \[ \sum_{n=1}^{\infty}(-1)^{n-1} b_{n}=\frac{1}{\sqrt{3}}-\frac{1}{\sqrt{4}}+\frac{1}{\sqrt{5}}-\frac{1}{\sqrt{6}}+\frac{1}{\sqrt{7}}-\cdots \] Identify \( b_{n} \). Evaluate the following limit. \[ \lim _{n \rightarrow \infty} b_{n} \] Since \( \lim _{n \rightarrow \infty} b_{n} \quad 0 \) and \( b_{n+1} \quad b_{n} \) for all \( n \),