List of top Engineering Mathematics Questions on Sequences and Series

Consider the infinite series \[ (P):\ \sum_{n=2}^{\infty}\frac{1}{(n\log n)^{1/n}}, \qquad (Q):\ \sum_{n=1}^{\infty}\frac{n^n}{(2n)!}. \] Then which one of the following statements is correct?

Consider the following two series:
\[ \textbf{P: } \sum_{n=1}^{\infty} \frac{1}{n} \qquad \textbf{Q: } \sum_{n=1}^{\infty} \frac{1}{n^2} \]
Choose the correct option from the following:

If the quadrature formula \[ \int_{-1}^{1} f(x)\,dx \;\approx\; \frac{1}{9}\Big(c_1 f(-1) + c_2 f\!\left(\tfrac{1}{2}\right) + c_3 f(1)\Big) \] is exact for all polynomials of degree less than or equal to $2$, then