(a) Show that the series $\sum \left[\sqrt{(n^3+1)} - \sqrt{n^3}\righ…

Previous year question for Engineering Mathematics-II.

Question

(a) Show that the series $\sum \left[\sqrt{(n^3+1)} - \sqrt{n^3}\right]$ is convergent.

(b) Discuss the convergence or divergence of the series $\sum \left(\frac{n}{n+1}\right)^{n^2}$

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